Daily Papers

Denoising diffusion (score-based) generative models have recently achieved significant accomplishments in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data into noise and a backward denoising process for sampling data from noise. Unfortunately, the generation process of current denoising diffusion models is notoriously slow due to the lengthy iterative noise estimations, which rely on cumbersome neural networks. It prevents the diffusion models from being widely deployed, especially on edge devices. Previous works accelerate the generation process of diffusion model (DM) via finding shorter yet effective sampling trajectories. However, they overlook the cost of noise estimation with a heavy network in every iteration. In this work, we accelerate generation from the perspective of compressing the noise estimation network. Due to the difficulty of retraining DMs, we exclude mainstream training-aware compression paradigms and introduce post-training quantization (PTQ) into DM acceleration. However, the output distributions of noise estimation networks change with time-step, making previous PTQ methods fail in DMs since they are designed for single-time step scenarios. To devise a DM-specific PTQ method, we explore PTQ on DM in three aspects: quantized operations, calibration dataset, and calibration metric. We summarize and use several observations derived from all-inclusive investigations to formulate our method, which especially targets the unique multi-time-step structure of DMs. Experimentally, our method can directly quantize full-precision DMs into 8-bit models while maintaining or even improving their performance in a training-free manner. Importantly, our method can serve as a plug-and-play module on other fast-sampling methods, e.g., DDIM. The code is available at https://github.com/42Shawn/PTQ4DM .

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Recently, conditional score-based diffusion models have gained significant attention in the field of supervised speech enhancement, yielding state-of-the-art performance. However, these methods may face challenges when generalising to unseen conditions. To address this issue, we introduce an alternative approach that operates in an unsupervised manner, leveraging the generative power of diffusion models. Specifically, in a training phase, a clean speech prior distribution is learnt in the short-time Fourier transform (STFT) domain using score-based diffusion models, allowing it to unconditionally generate clean speech from Gaussian noise. Then, we develop a posterior sampling methodology for speech enhancement by combining the learnt clean speech prior with a noise model for speech signal inference. The noise parameters are simultaneously learnt along with clean speech estimation through an iterative expectationmaximisation (EM) approach. To the best of our knowledge, this is the first work exploring diffusion-based generative models for unsupervised speech enhancement, demonstrating promising results compared to a recent variational auto-encoder (VAE)-based unsupervised approach and a state-of-the-art diffusion-based supervised method. It thus opens a new direction for future research in unsupervised speech enhancement.

Crystal structure generation is a foundational challenge in materials discovery, particularly in designing functional inorganic crystalline materials with desired properties. Most existing diffusion-based generative models for crystals rely on complex, hand-crafted priors and modular architectures to separately model atom types, atomic positions, and lattice parameters. These methods often require customized diffusion processes and conditional denoising, which can introduce additional model complexities and inconsistencies. Here we introduce DiffCrysGen, a fully data-driven, score-based diffusion model that jointly learns the distribution of all structural components in crystalline materials. With crystal structure representation as unified 2D matrices, DiffCrysGen bypasses the need for task-specific priors or decoupled modules, enabling end-to-end generation of atom types, fractional coordinates, and lattice parameters within a single framework. Our model learns crystallographic symmetry and chemical validity directly from large-scale datasets, allowing it to scale to complex materials discovery tasks. As a demonstration, we applied DiffCrysGen to the design of rare-earth-free magnetic materials with high saturation magnetization, showing its effectiveness in generating stable, diverse, and property-aligned candidates for sustainable magnet applications.

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images. Likelihood-based GMs are attractive due to the possibility to generate new data by a single model evaluation. However, they typically achieve lower sample quality compared to state-of-the-art score-based diffusion models (DMs). This paper provides a significant step in the direction of addressing this limitation. The idea is to borrow one of the strengths of score-based DMs, which is the ability to perform accurate density estimation in low-density regions and to address manifold overfitting by means of data mollification. We connect data mollification through the addition of Gaussian noise to Gaussian homotopy, which is a well-known technique to improve optimization. Data mollification can be implemented by adding one line of code in the optimization loop, and we demonstrate that this provides a boost in generation quality of likelihood-based GMs, without computational overheads. We report results on image data sets with popular likelihood-based GMs, including variants of variational autoencoders and normalizing flows, showing large improvements in FID score.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

Despite the tremendous success of diffusion generative models in text-to-image generation, replicating this success in the domain of image compression has proven difficult. In this paper, we demonstrate that diffusion can significantly improve perceptual quality at a given bit-rate, outperforming state-of-the-art approaches PO-ELIC and HiFiC as measured by FID score. This is achieved using a simple but theoretically motivated two-stage approach combining an autoencoder targeting MSE followed by a further score-based decoder. However, as we will show, implementation details matter and the optimal design decisions can differ greatly from typical text-to-image models.

Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the complex short-time Fourier transform (STFT) domain, proposing a novel training task for speech enhancement using a complex-valued deep neural network. We derive this training task within the formalism of stochastic differential equations (SDEs), thereby enabling the use of predictor-corrector samplers. We provide alternative formulations inspired by previous publications on using generative diffusion models for speech enhancement, avoiding the need for any prior assumptions on the noise distribution and making the training task purely generative which, as we show, results in improved enhancement performance.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models and Score-based Generative Models, where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance on the E(3) group can keep the physical stability of the frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation.

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Score-based generative models, commonly referred to as diffusion models, have proven to be successful at generating text and image data. However, their adaptation to mixed-type tabular data remains underexplored. In this work, we propose CDTD, a Continuous Diffusion model for mixed-type Tabular Data. CDTD is based on a novel combination of score matching and score interpolation to enforce a unified continuous noise distribution for both continuous and categorical features. We explicitly acknowledge the necessity of homogenizing distinct data types by relying on model-specific loss calibration and initialization schemes.To further address the high heterogeneity in mixed-type tabular data, we introduce adaptive feature- or type-specific noise schedules. These ensure balanced generative performance across features and optimize the allocation of model capacity across features and diffusion time. Our experimental results show that CDTD consistently outperforms state-of-the-art benchmark models, captures feature correlations exceptionally well, and that heterogeneity in the noise schedule design boosts sample quality. Replication code is available at https://github.com/muellermarkus/cdtd.

Score-based generative models like the diffusion model have been testified to be effective in modeling multi-modal data from image generation to reinforcement learning (RL). However, the inference process of diffusion model can be slow, which hinders its usage in RL with iterative sampling. We propose to apply the consistency model as an efficient yet expressive policy representation, namely consistency policy, with an actor-critic style algorithm for three typical RL settings: offline, offline-to-online and online. For offline RL, we demonstrate the expressiveness of generative models as policies from multi-modal data. For offline-to-online RL, the consistency policy is shown to be more computational efficient than diffusion policy, with a comparable performance. For online RL, the consistency policy demonstrates significant speedup and even higher average performances than the diffusion policy.

This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling. The code is available at https://github.com/checkcrab/SDSB.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

Training large neural networks with end-to-end backpropagation creates significant memory bottlenecks, limiting accessibility to state-of-the-art AI research. We propose DiffusionBlocks, a novel training framework that interprets neural network blocks as performing denoising operations in a continuous-time diffusion process. By partitioning the network into independently trainable blocks and optimizing noise level assignments based on equal cumulative probability mass, our approach achieves significant memory efficiency while maintaining competitive performance compared to traditional backpropagation in generative tasks. Experiments on image generation and language modeling tasks demonstrate memory reduction proportional to the number of blocks while achieving superior performance. DiffusionBlocks provides a promising pathway for democratizing access to large-scale neural network training with limited computational resources.

Idempotent generative networks (IGNs) are a new line of generative models based on idempotent mapping to a target manifold. IGNs support both single-and multi-step generation, allowing for a flexible trade-off between computational cost and sample quality. But similar to Generative Adversarial Networks (GANs), conventional IGNs require adversarial training and are prone to training instabilities and mode collapse. Diffusion and score-based models are popular approaches to generative modeling that iteratively transport samples from one distribution, usually a Gaussian, to a target data distribution. These models have gained popularity due to their stable training dynamics and high-fidelity generation quality. However, this stability and quality come at the cost of high computational cost, as the data must be transported incrementally along the entire trajectory. New sampling methods, model distillation, and consistency models have been developed to reduce the sampling cost and even perform one-shot sampling from diffusion models. In this work, we unite diffusion and IGNs by distilling idempotent models from diffusion model scores, called SIGN. Our proposed method is highly stable and does not require adversarial losses. We provide a theoretical analysis of our proposed score-based training methods and empirically show that IGNs can be effectively distilled from a pre-trained diffusion model, enabling faster inference than iterative score-based models. SIGNs can perform multi-step sampling, allowing users to trade off quality for efficiency. These models operate directly on the source domain; they can project corrupted or alternate distributions back onto the target manifold, enabling zero-shot editing of inputs. We validate our models on multiple image datasets, achieving state-of-the-art results for idempotent models on the CIFAR and CelebA datasets.

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than standard diffusion models, makes possible a modular study of various design choices impacting generative models built on dynamical transport: using discrete vs. continuous time learning, deciding the objective for the model to learn, choosing the interpolant connecting the distributions, and deploying a deterministic or stochastic sampler. By carefully introducing the above ingredients, SiT surpasses DiT uniformly across model sizes on the conditional ImageNet 256x256 benchmark using the exact same backbone, number of parameters, and GFLOPs. By exploring various diffusion coefficients, which can be tuned separately from learning, SiT achieves an FID-50K score of 2.06.

We argue that the theory and practice of diffusion-based generative models are currently unnecessarily convoluted and seek to remedy the situation by presenting a design space that clearly separates the concrete design choices. This lets us identify several changes to both the sampling and training processes, as well as preconditioning of the score networks. Together, our improvements yield new state-of-the-art FID of 1.79 for CIFAR-10 in a class-conditional setting and 1.97 in an unconditional setting, with much faster sampling (35 network evaluations per image) than prior designs. To further demonstrate their modular nature, we show that our design changes dramatically improve both the efficiency and quality obtainable with pre-trained score networks from previous work, including improving the FID of a previously trained ImageNet-64 model from 2.07 to near-SOTA 1.55, and after re-training with our proposed improvements to a new SOTA of 1.36.

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations. The summary of existing methods metioned in this survey is in https://github.com/zhejiangzhuque/Diffusion-based-Graph-Generative-Methods.

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and employed in practice, the theoretical understandings about convergence properties of the probability flow ODE are still quite limited. In this paper, we provide the first non-asymptotic convergence analysis for a general class of probability flow ODE samplers in 2-Wasserstein distance, assuming accurate score estimates. We then consider various examples and establish results on the iteration complexity of the corresponding ODE-based samplers.

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term K-RCPS, which allows to (i) provide entrywise calibrated intervals for future samples of any diffusion model, and (ii) control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Score-based Generative Models (SGMs) have achieved state-of-the-art synthesis results on diverse tasks. However, the current design space of the forward diffusion process is largely unexplored and often relies on physical intuition or simplifying assumptions. Leveraging results from the design of scalable Bayesian posterior samplers, we present a complete recipe for constructing forward processes in SGMs, all of which are guaranteed to converge to the target distribution of interest. We show that several existing SGMs can be cast as specific instantiations of this parameterization. Furthermore, building on this recipe, we construct a novel SGM: Phase Space Langevin Diffusion (PSLD), which performs score-based modeling in a space augmented with auxiliary variables akin to a physical phase space. We show that PSLD outperforms competing baselines in terms of sample quality and the speed-vs-quality tradeoff across different samplers on various standard image synthesis benchmarks. Moreover, we show that PSLD achieves sample quality comparable to state-of-the-art SGMs (FID: 2.10 on unconditional CIFAR-10 generation), providing an attractive alternative as an SGM backbone for further development. We will publish our code and model checkpoints for reproducibility at https://github.com/mandt-lab/PSLD.

Self-supervised learning (SSL) has revolutionized representation learning in Remote Sensing (RS), advancing Geospatial Foundation Models (GFMs) to leverage vast unlabeled satellite imagery for diverse downstream tasks. Currently, GFMs primarily focus on discriminative objectives, such as contrastive learning or masked image modeling, owing to their proven success in learning transferable representations. However, generative diffusion models--which demonstrate the potential to capture multi-grained semantics essential for RS tasks during image generation--remain underexplored for discriminative applications. This prompts the question: can generative diffusion models also excel and serve as GFMs with sufficient discriminative power? In this work, we answer this question with SatDiFuser, a framework that transforms a diffusion-based generative geospatial foundation model into a powerful pretraining tool for discriminative RS. By systematically analyzing multi-stage, noise-dependent diffusion features, we develop three fusion strategies to effectively leverage these diverse representations. Extensive experiments on remote sensing benchmarks show that SatDiFuser outperforms state-of-the-art GFMs, achieving gains of up to +5.7% mIoU in semantic segmentation and +7.9% F1-score in classification, demonstrating the capacity of diffusion-based generative foundation models to rival or exceed discriminative GFMs. Code will be released.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Diffusion-based generative models have recently achieved remarkable results in speech and vocal enhancement due to their ability to model complex speech data distributions. While these models generalize well to unseen acoustic environments, they may not achieve the same level of fidelity as the discriminative models specifically trained to enhance particular acoustic conditions. In this paper, we propose Ex-Diff, a novel score-based diffusion model that integrates the latent representations produced by a discriminative model to improve speech and vocal enhancement, which combines the strengths of both generative and discriminative models. Experimental results on the widely used MUSDB dataset show relative improvements of 3.7% in SI-SDR and 10.0% in SI-SIR compared to the baseline diffusion model for speech and vocal enhancement tasks, respectively. Additionally, case studies are provided to further illustrate and analyze the complementary nature of generative and discriminative models in this context.

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic differential equations (SDEs) and ordinary differential equations (ODEs). Empirically, it has been reported that ODE based samples are inferior to SDE based samples. In this paper we rigorously describe the range of dynamics and approximations that arise when training score-based diffusion models, including the true SDE dynamics, the neural approximations, the various approximate particle dynamics that result, as well as their associated Fokker--Planck equations and the neural network approximations of these Fokker--Planck equations. We systematically analyse the difference between the ODE and SDE dynamics of score-based diffusion models, and link it to an associated Fokker--Planck equation. We derive a theoretical upper bound on the Wasserstein 2-distance between the ODE- and SDE-induced distributions in terms of a Fokker--Planck residual. We also show numerically that conventional score-based diffusion models can exhibit significant differences between ODE- and SDE-induced distributions which we demonstrate using explicit comparisons. Moreover, we show numerically that reducing the Fokker--Planck residual by adding it as an additional regularisation term leads to closing the gap between ODE- and SDE-induced distributions. Our experiments suggest that this regularisation can improve the distribution generated by the ODE, however that this can come at the cost of degraded SDE sample quality.

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

Score-based diffusion models have captured widespread attention and funded fast progress of recent vision generative tasks. In this paper, we focus on diffusion model backbone which has been much neglected before. We systematically explore vision Transformers as diffusion learners for various generative tasks. With our improvements the performance of vanilla ViT-based backbone (IU-ViT) is boosted to be on par with traditional U-Net-based methods. We further provide a hypothesis on the implication of disentangling the generative backbone as an encoder-decoder structure and show proof-of-concept experiments verifying the effectiveness of a stronger encoder for generative tasks with ASymmetriC ENcoder Decoder (ASCEND). Our improvements achieve competitive results on CIFAR-10, CelebA, LSUN, CUB Bird and large-resolution text-to-image tasks. To the best of our knowledge, we are the first to successfully train a single diffusion model on text-to-image task beyond 64x64 resolution. We hope this will motivate people to rethink the modeling choices and the training pipelines for diffusion-based generative models.

In this work, we define a diffusion-based generative model capable of both music synthesis and source separation by learning the score of the joint probability density of sources sharing a context. Alongside the classic total inference tasks (i.e., generating a mixture, separating the sources), we also introduce and experiment on the partial generation task of source imputation, where we generate a subset of the sources given the others (e.g., play a piano track that goes well with the drums). Additionally, we introduce a novel inference method for the separation task based on Dirac likelihood functions. We train our model on Slakh2100, a standard dataset for musical source separation, provide qualitative results in the generation settings, and showcase competitive quantitative results in the source separation setting. Our method is the first example of a single model that can handle both generation and separation tasks, thus representing a step toward general audio models.

While generative diffusion models excel in producing high-quality images, they can also be misused to mimic authorized images, posing a significant threat to AI systems. Efforts have been made to add calibrated perturbations to protect images from diffusion-based mimicry pipelines. However, most of the existing methods are too ineffective and even impractical to be used by individual users due to their high computation and memory requirements. In this work, we present novel findings on attacking latent diffusion models (LDM) and propose new plug-and-play strategies for more effective protection. In particular, we explore the bottleneck in attacking an LDM, discovering that the encoder module rather than the denoiser module is the vulnerable point. Based on this insight, we present our strategy using Score Distillation Sampling (SDS) to double the speed of protection and reduce memory occupation by half without compromising its strength. Additionally, we provide a robust protection strategy by counterintuitively minimizing the semantic loss, which can assist in generating more natural perturbations. Finally, we conduct extensive experiments to substantiate our findings and comprehensively evaluate our newly proposed strategies. We hope our insights and protective measures can contribute to better defense against malicious diffusion-based mimicry, advancing the development of secure AI systems. The code is available in https://github.com/xavihart/Diff-Protect

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations (SDE) model is a continuous-time diffusion model framework that enjoys many benefits, but the originally proposed SDEs are not naturally designed for modeling discrete data. To develop generative SDE models for discrete data such as biological sequences, here we introduce a diffusion process defined in the probability simplex space with stationary distribution being the Dirichlet distribution. This makes diffusion in continuous space natural for modeling discrete data. We refer to this approach as Dirchlet diffusion score model. We demonstrate that this technique can generate samples that satisfy hard constraints using a Sudoku generation task. This generative model can also solve Sudoku, including hard puzzles, without additional training. Finally, we applied this approach to develop the first human promoter DNA sequence design model and showed that designed sequences share similar properties with natural promoter sequences.

Removing background noise from speech audio has been the subject of considerable effort, especially in recent years due to the rise of virtual communication and amateur recordings. Yet background noise is not the only unpleasant disturbance that can prevent intelligibility: reverb, clipping, codec artifacts, problematic equalization, limited bandwidth, or inconsistent loudness are equally disturbing and ubiquitous. In this work, we propose to consider the task of speech enhancement as a holistic endeavor, and present a universal speech enhancement system that tackles 55 different distortions at the same time. Our approach consists of a generative model that employs score-based diffusion, together with a multi-resolution conditioning network that performs enhancement with mixture density networks. We show that this approach significantly outperforms the state of the art in a subjective test performed by expert listeners. We also show that it achieves competitive objective scores with just 4-8 diffusion steps, despite not considering any particular strategy for fast sampling. We hope that both our methodology and technical contributions encourage researchers and practitioners to adopt a universal approach to speech enhancement, possibly framing it as a generative task.

Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are essential, making prior methods potentially unsuitable in such contexts. Moreover, while trivial adaptations are available, empirical investigations reveal their limited efficacy as they do not properly model the interplay among graph components. To address this, we propose a joint score-based model of nodes and edges for graph generation that considers all graph components. Our approach offers two key novelties: (i) node and edge attributes are combined in an attention module that generates samples based on the two ingredients; and (ii) node, edge and adjacency information are mutually dependent during the graph diffusion process. We evaluate our method on challenging benchmarks involving real-world and synthetic datasets in which edge features are crucial. Additionally, we introduce a new synthetic dataset that incorporates edge values. Furthermore, we propose a novel application that greatly benefits from the method due to its nature: the generation of traffic scenes represented as graphs. Our method outperforms other graph generation methods, demonstrating a significant advantage in edge-related measures.

Recent text-to-image diffusion-based generative models have the stunning ability to generate highly detailed and photo-realistic images and achieve state-of-the-art low FID scores on challenging image generation benchmarks. However, one of the primary failure modes of these text-to-image generative models is in composing attributes, objects, and their associated relationships accurately into an image. In our paper, we investigate this compositionality-based failure mode and highlight that imperfect text conditioning with CLIP text-encoder is one of the primary reasons behind the inability of these models to generate high-fidelity compositional scenes. In particular, we show that (i) there exists an optimal text-embedding space that can generate highly coherent compositional scenes which shows that the output space of the CLIP text-encoder is sub-optimal, and (ii) we observe that the final token embeddings in CLIP are erroneous as they often include attention contributions from unrelated tokens in compositional prompts. Our main finding shows that the best compositional improvements can be achieved (without harming the model's FID scores) by fine-tuning {\it only} a simple linear projection on CLIP's representation space in Stable-Diffusion variants using a small set of compositional image-text pairs. This result demonstrates that the sub-optimality of the CLIP's output space is a major error source. We also show that re-weighting the erroneous attention contributions in CLIP can also lead to improved compositional performances, however these improvements are often less significant than those achieved by solely learning a linear projection head, highlighting erroneous attentions to be only a minor error source.

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Text-to-image diffusion models have demonstrated an impressive ability to produce high-quality outputs. However, they often struggle to accurately follow fine-grained spatial information in an input text. To this end, we propose a compositional approach for text-to-image generation based on two stages. In the first stage, we design a diffusion-based generative model to produce one or more aligned intermediate representations (such as depth or segmentation maps) conditioned on text. In the second stage, we map these representations, together with the text, to the final output image using a separate diffusion-based generative model. Our findings indicate that such compositional approach can improve image generation, resulting in a notable improvement in FID score and a comparable CLIP score, when compared to the standard non-compositional baseline.

Although recent mainstream waveform-domain end-to-end (E2E) neural audio codecs achieve impressive coded audio quality with a very low bitrate, the quality gap between the coded and natural audio is still significant. A generative adversarial network (GAN) training is usually required for these E2E neural codecs because of the difficulty of direct phase modeling. However, such adversarial learning hinders these codecs from preserving the original phase information. To achieve human-level naturalness with a reasonable bitrate, preserve the original phase, and get rid of the tricky and opaque GAN training, we develop a score-based diffusion post-filter (SPF) in the complex spectral domain and combine our previous AudioDec with the SPF to propose ScoreDec, which can be trained using only spectral and score-matching losses. Both the objective and subjective experimental results show that ScoreDec with a 24~kbps bitrate encodes and decodes full-band 48~kHz speech with human-level naturalness and well-preserved phase information.

We propose a new policy representation based on score-based diffusion models (SDMs). We apply our new policy representation in the domain of Goal-Conditioned Imitation Learning (GCIL) to learn general-purpose goal-specified policies from large uncurated datasets without rewards. Our new goal-conditioned policy architecture "BEhavior generation with ScOre-based Diffusion Policies" (BESO) leverages a generative, score-based diffusion model as its policy. BESO decouples the learning of the score model from the inference sampling process, and, hence allows for fast sampling strategies to generate goal-specified behavior in just 3 denoising steps, compared to 30+ steps of other diffusion based policies. Furthermore, BESO is highly expressive and can effectively capture multi-modality present in the solution space of the play data. Unlike previous methods such as Latent Plans or C-Bet, BESO does not rely on complex hierarchical policies or additional clustering for effective goal-conditioned behavior learning. Finally, we show how BESO can even be used to learn a goal-independent policy from play-data using classifier-free guidance. To the best of our knowledge this is the first work that a) represents a behavior policy based on such a decoupled SDM b) learns an SDM based policy in the domain of GCIL and c) provides a way to simultaneously learn a goal-dependent and a goal-independent policy from play-data. We evaluate BESO through detailed simulation and show that it consistently outperforms several state-of-the-art goal-conditioned imitation learning methods on challenging benchmarks. We additionally provide extensive ablation studies and experiments to demonstrate the effectiveness of our method for goal-conditioned behavior generation. Demonstrations and Code are available at https://intuitive-robots.github.io/beso-website/

Conditioning image generation facilitates seamless editing and the creation of photorealistic images. However, conditioning on noisy or Out-of-Distribution (OoD) images poses significant challenges, particularly in balancing fidelity to the input and realism of the output. We introduce Confident Ordinary Differential Editing (CODE), a novel approach for image synthesis that effectively handles OoD guidance images. Utilizing a diffusion model as a generative prior, CODE enhances images through score-based updates along the probability-flow Ordinary Differential Equation (ODE) trajectory. This method requires no task-specific training, no handcrafted modules, and no assumptions regarding the corruptions affecting the conditioning image. Our method is compatible with any diffusion model. Positioned at the intersection of conditional image generation and blind image restoration, CODE operates in a fully blind manner, relying solely on a pre-trained generative model. Our method introduces an alternative approach to blind restoration: instead of targeting a specific ground truth image based on assumptions about the underlying corruption, CODE aims to increase the likelihood of the input image while maintaining fidelity. This results in the most probable in-distribution image around the input. Our contributions are twofold. First, CODE introduces a novel editing method based on ODE, providing enhanced control, realism, and fidelity compared to its SDE-based counterpart. Second, we introduce a confidence interval-based clipping method, which improves CODE's effectiveness by allowing it to disregard certain pixels or information, thus enhancing the restoration process in a blind manner. Experimental results demonstrate CODE's effectiveness over existing methods, particularly in scenarios involving severe degradation or OoD inputs.

While likelihood-based generative models, particularly diffusion and autoregressive models, have achieved remarkable fidelity in visual generation, the maximum likelihood estimation (MLE) objective inherently suffers from a mode-covering tendency that limits the generation quality under limited model capacity. In this work, we propose Direct Discriminative Optimization (DDO) as a unified framework that bridges likelihood-based generative training and the GAN objective to bypass this fundamental constraint. Our key insight is to parameterize a discriminator implicitly using the likelihood ratio between a learnable target model and a fixed reference model, drawing parallels with the philosophy of Direct Preference Optimization (DPO). Unlike GANs, this parameterization eliminates the need for joint training of generator and discriminator networks, allowing for direct, efficient, and effective finetuning of a well-trained model to its full potential beyond the limits of MLE. DDO can be performed iteratively in a self-play manner for progressive model refinement, with each round requiring less than 1% of pretraining epochs. Our experiments demonstrate the effectiveness of DDO by significantly advancing the previous SOTA diffusion model EDM, reducing FID scores from 1.79/1.58 to new records of 1.30/0.97 on CIFAR-10/ImageNet-64 datasets, and by consistently improving both guidance-free and CFG-enhanced FIDs of visual autoregressive models on ImageNet 256times256.

In this work we develop 3D Paintbrush, a technique for automatically texturing local semantic regions on meshes via text descriptions. Our method is designed to operate directly on meshes, producing texture maps which seamlessly integrate into standard graphics pipelines. We opt to simultaneously produce a localization map (to specify the edit region) and a texture map which conforms to it. This synergistic approach improves the quality of both the localization and the stylization. To enhance the details and resolution of the textured area, we leverage multiple stages of a cascaded diffusion model to supervise our local editing technique with generative priors learned from images at different resolutions. Our technique, referred to as Cascaded Score Distillation (CSD), simultaneously distills scores at multiple resolutions in a cascaded fashion, enabling control over both the granularity and global understanding of the supervision. We demonstrate the effectiveness of 3D Paintbrush to locally texture a variety of shapes within different semantic regions. Project page: https://threedle.github.io/3d-paintbrush

Sound content is an indispensable element for multimedia works such as video games, music, and films. Recent high-quality diffusion-based sound generation models can serve as valuable tools for the creators. However, despite producing high-quality sounds, these models often suffer from slow inference speeds. This drawback burdens creators, who typically refine their sounds through trial and error to align them with their artistic intentions. To address this issue, we introduce Sound Consistency Trajectory Models (SoundCTM). Our model enables flexible transitioning between high-quality 1-step sound generation and superior sound quality through multi-step generation. This allows creators to initially control sounds with 1-step samples before refining them through multi-step generation. While CTM fundamentally achieves flexible 1-step and multi-step generation, its impressive performance heavily depends on an additional pretrained feature extractor and an adversarial loss, which are expensive to train and not always available in other domains. Thus, we reframe CTM's training framework and introduce a novel feature distance by utilizing the teacher's network for a distillation loss. Additionally, while distilling classifier-free guided trajectories, we train conditional and unconditional student models simultaneously and interpolate between these models during inference. We also propose training-free controllable frameworks for SoundCTM, leveraging its flexible sampling capability. SoundCTM achieves both promising 1-step and multi-step real-time sound generation without using any extra off-the-shelf networks. Furthermore, we demonstrate SoundCTM's capability of controllable sound generation in a training-free manner.

At high-energy collider experiments, generative models can be used for a wide range of tasks, including fast detector simulations, unfolding, searches of physics beyond the Standard Model, and inference tasks. In particular, it has been demonstrated that score-based diffusion models can generate high-fidelity and accurate samples of jets or collider events. This work expands on previous generative models in three distinct ways. First, our model is trained to generate entire collider events, including all particle species with complete kinematic information. We quantify how well the model learns event-wide constraints such as the conservation of momentum and discrete quantum numbers. We focus on the events at the future Electron-Ion Collider, but we expect that our results can be extended to proton-proton and heavy-ion collisions. Second, previous generative models often relied on image-based techniques. The sparsity of the data can negatively affect the fidelity and sampling time of the model. We address these issues using point clouds and a novel architecture combining edge creation with transformer modules called Point Edge Transformers. Third, we adapt the foundation model OmniLearn, to generate full collider events. This approach may indicate a transition toward adapting and fine-tuning foundation models for downstream tasks instead of training new models from scratch.

Score-based or diffusion models generate high-quality tabular data, surpassing GAN-based and VAE-based models. However, these methods require substantial training time. In this paper, we introduce RecTable, which uses the rectified flow modeling, applied in such as text-to-image generation and text-to-video generation. RecTable features a simple architecture consisting of a few stacked gated linear unit blocks. Additionally, our training strategies are also simple, incorporating a mixed-type noise distribution and a logit-normal timestep distribution. Our experiments demonstrate that RecTable achieves competitive performance compared to the several state-of-the-art diffusion and score-based models while reducing the required training time. Our code is available at https://github.com/fmp453/rectable.

Since their introduction, diffusion models have quickly become the prevailing approach to generative modeling in many domains. They can be interpreted as learning the gradients of a time-varying sequence of log-probability density functions. This interpretation has motivated classifier-based and classifier-free guidance as methods for post-hoc control of diffusion models. In this work, we build upon these ideas using the score-based interpretation of diffusion models, and explore alternative ways to condition, modify, and reuse diffusion models for tasks involving compositional generation and guidance. In particular, we investigate why certain types of composition fail using current techniques and present a number of solutions. We conclude that the sampler (not the model) is responsible for this failure and propose new samplers, inspired by MCMC, which enable successful compositional generation. Further, we propose an energy-based parameterization of diffusion models which enables the use of new compositional operators and more sophisticated, Metropolis-corrected samplers. Intriguingly we find these samplers lead to notable improvements in compositional generation across a wide set of problems such as classifier-guided ImageNet modeling and compositional text-to-image generation.

Recent advances in tabular data generation have greatly enhanced synthetic data quality. However, extending diffusion models to tabular data is challenging due to the intricately varied distributions and a blend of data types of tabular data. This paper introduces Tabsyn, a methodology that synthesizes tabular data by leveraging a diffusion model within a variational autoencoder (VAE) crafted latent space. The key advantages of the proposed Tabsyn include (1) Generality: the ability to handle a broad spectrum of data types by converting them into a single unified space and explicitly capture inter-column relations; (2) Quality: optimizing the distribution of latent embeddings to enhance the subsequent training of diffusion models, which helps generate high-quality synthetic data, (3) Speed: much fewer number of reverse steps and faster synthesis speed than existing diffusion-based methods. Extensive experiments on six datasets with five metrics demonstrate that Tabsyn outperforms existing methods. Specifically, it reduces the error rates by 86% and 67% for column-wise distribution and pair-wise column correlation estimations compared with the most competitive baselines.

Recently, denoising diffusion probabilistic models and generative score matching have shown high potential in modelling complex data distributions while stochastic calculus has provided a unified point of view on these techniques allowing for flexible inference schemes. In this paper we introduce Grad-TTS, a novel text-to-speech model with score-based decoder producing mel-spectrograms by gradually transforming noise predicted by encoder and aligned with text input by means of Monotonic Alignment Search. The framework of stochastic differential equations helps us to generalize conventional diffusion probabilistic models to the case of reconstructing data from noise with different parameters and allows to make this reconstruction flexible by explicitly controlling trade-off between sound quality and inference speed. Subjective human evaluation shows that Grad-TTS is competitive with state-of-the-art text-to-speech approaches in terms of Mean Opinion Score. We will make the code publicly available shortly.

Molecule generation is advancing rapidly in chemical discovery and drug design. Flow matching methods have recently set the state of the art (SOTA) in unconditional molecule generation, surpassing score-based diffusion models. However, diffusion models still lead in property-guided generation. In this work, we introduce PropMolFlow, a novel approach for property-guided molecule generation based on geometry-complete SE(3)-equivariant flow matching. Integrating five different property embedding methods with a Gaussian expansion of scalar properties, PropMolFlow outperforms previous SOTA diffusion models in conditional molecule generation across various properties while preserving the stability and validity of the generated molecules, consistent with its unconditional counterpart. Additionally, it enables faster inference with significantly fewer time steps compared to baseline models. We highlight the importance of validating the properties of generated molecules through DFT calculations performed at the same level of theory as the training data. Specifically, our analysis identifies properties that require DFT validation and others where a pretrained SE(3) geometric vector perceptron regressors provide sufficiently accurate predictions on generated molecules. Furthermore, we introduce a new property metric designed to assess the model's ability to propose molecules with underrepresented property values, assessing its capacity for out-of-distribution generalization. Our findings reveal shortcomings in existing structural metrics, which mistakenly validate open-shell molecules or molecules with invalid valence-charge configurations, underscoring the need for improved evaluation frameworks. Overall, this work paves the way for developing targeted property-guided generation methods, enhancing the design of molecular generative models for diverse applications.

The training of score-based diffusion models (SDMs) is based on score matching. The challenge of score matching is that it includes a computationally expensive Jacobian trace. While several methods have been proposed to avoid this computation, each has drawbacks, such as instability during training and approximating the learning as learning a denoising vector field rather than a true score. We propose a novel score matching variant, local curvature smoothing with Stein's identity (LCSS). The LCSS bypasses the Jacobian trace by applying Stein's identity, enabling regularization effectiveness and efficient computation. We show that LCSS surpasses existing methods in sample generation performance and matches the performance of denoising score matching, widely adopted by most SDMs, in evaluations such as FID, Inception score, and bits per dimension. Furthermore, we show that LCSS enables realistic image generation even at a high resolution of 1024 times 1024.

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. The PyTorch implementation is available at https://github.com/mingyuanzhou/SiD

We present a novel generative approach based on Denoising Diffusion Models (DDMs), which produces high-quality image samples along with their losslessly compressed bit-stream representations. This is obtained by replacing the standard Gaussian noise sampling in the reverse diffusion with a selection of noise samples from pre-defined codebooks of fixed iid Gaussian vectors. Surprisingly, we find that our method, termed Denoising Diffusion Codebook Model (DDCM), retains sample quality and diversity of standard DDMs, even for extremely small codebooks. We leverage DDCM and pick the noises from the codebooks that best match a given image, converting our generative model into a highly effective lossy image codec achieving state-of-the-art perceptual image compression results. More generally, by setting other noise selections rules, we extend our compression method to any conditional image generation task (e.g., image restoration), where the generated images are produced jointly with their condensed bit-stream representations. Our work is accompanied by a mathematical interpretation of the proposed compressed conditional generation schemes, establishing a connection with score-based approximations of posterior samplers for the tasks considered.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but recent reports of memorization of the training set raise the question of whether these networks are learning the "true" continuous density of the data. Here, we show that two DNNs trained on non-overlapping subsets of a dataset learn nearly the same score function, and thus the same density, when the number of training images is large enough. In this regime of strong generalization, diffusion-generated images are distinct from the training set, and are of high visual quality, suggesting that the inductive biases of the DNNs are well-aligned with the data density. We analyze the learned denoising functions and show that the inductive biases give rise to a shrinkage operation in a basis adapted to the underlying image. Examination of these bases reveals oscillating harmonic structures along contours and in homogeneous regions. We demonstrate that trained denoisers are inductively biased towards these geometry-adaptive harmonic bases since they arise not only when the network is trained on photographic images, but also when it is trained on image classes supported on low-dimensional manifolds for which the harmonic basis is suboptimal. Finally, we show that when trained on regular image classes for which the optimal basis is known to be geometry-adaptive and harmonic, the denoising performance of the networks is near-optimal.

Text-to-3D generation has shown rapid progress in recent days with the advent of score distillation, a methodology of using pretrained text-to-2D diffusion models to optimize neural radiance field (NeRF) in the zero-shot setting. However, the lack of 3D awareness in the 2D diffusion models destabilizes score distillation-based methods from reconstructing a plausible 3D scene. To address this issue, we propose 3DFuse, a novel framework that incorporates 3D awareness into pretrained 2D diffusion models, enhancing the robustness and 3D consistency of score distillation-based methods. We realize this by first constructing a coarse 3D structure of a given text prompt and then utilizing projected, view-specific depth map as a condition for the diffusion model. Additionally, we introduce a training strategy that enables the 2D diffusion model learns to handle the errors and sparsity within the coarse 3D structure for robust generation, as well as a method for ensuring semantic consistency throughout all viewpoints of the scene. Our framework surpasses the limitations of prior arts, and has significant implications for 3D consistent generation of 2D diffusion models.

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution of real molecules. Then, we follow the neural empirical Bayes framework [Saremi and Hyvarinen, 2019] and generate molecules in two steps: (i) sample noisy density grids from a smooth distribution via underdamped Langevin Markov chain Monte Carlo, and (ii) recover the ``clean'' molecule by denoising the noisy grid with a single step. Our method, VoxMol, generates molecules in a fundamentally different way than the current state of the art (i.e., diffusion models applied to atom point clouds). It differs in terms of the data representation, the noise model, the network architecture and the generative modeling algorithm. VoxMol achieves comparable results to state of the art on unconditional 3D molecule generation while being simpler to train and faster to generate molecules.

Despite advances in diffusion-based text-to-music (TTM) methods, efficient, high-quality generation remains a challenge. We introduce Presto!, an approach to inference acceleration for score-based diffusion transformers via reducing both sampling steps and cost per step. To reduce steps, we develop a new score-based distribution matching distillation (DMD) method for the EDM-family of diffusion models, the first GAN-based distillation method for TTM. To reduce the cost per step, we develop a simple, but powerful improvement to a recent layer distillation method that improves learning via better preserving hidden state variance. Finally, we combine our step and layer distillation methods together for a dual-faceted approach. We evaluate our step and layer distillation methods independently and show each yield best-in-class performance. Our combined distillation method can generate high-quality outputs with improved diversity, accelerating our base model by 10-18x (230/435ms latency for 32 second mono/stereo 44.1kHz, 15x faster than comparable SOTA) -- the fastest high-quality TTM to our knowledge. Sound examples can be found at https://presto-music.github.io/web/.

Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with proper designs, the evolution of neural networks during training can be accurately modeled by a series of kernel regression tasks. Furthermore, by applying an early-stopping rule for gradient descent and leveraging recent developments in neural tangent kernels, we establish the first generalization error (sample complexity) bounds for learning the score function with neural networks, despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.

Encouraged by the growing availability of pre-trained 2D diffusion models, image-to-3D generation by leveraging Score Distillation Sampling (SDS) is making remarkable progress. Most existing methods combine novel-view lifting from 2D diffusion models which usually take the reference image as a condition while applying hard L2 image supervision at the reference view. Yet heavily adhering to the image is prone to corrupting the inductive knowledge of the 2D diffusion model leading to flat or distorted 3D generation frequently. In this work, we reexamine image-to-3D in a novel perspective and present Isotropic3D, an image-to-3D generation pipeline that takes only an image CLIP embedding as input. Isotropic3D allows the optimization to be isotropic w.r.t. the azimuth angle by solely resting on the SDS loss. The core of our framework lies in a two-stage diffusion model fine-tuning. Firstly, we fine-tune a text-to-3D diffusion model by substituting its text encoder with an image encoder, by which the model preliminarily acquires image-to-image capabilities. Secondly, we perform fine-tuning using our Explicit Multi-view Attention (EMA) which combines noisy multi-view images with the noise-free reference image as an explicit condition. CLIP embedding is sent to the diffusion model throughout the whole process while reference images are discarded once after fine-tuning. As a result, with a single image CLIP embedding, Isotropic3D is capable of generating multi-view mutually consistent images and also a 3D model with more symmetrical and neat content, well-proportioned geometry, rich colored texture, and less distortion compared with existing image-to-3D methods while still preserving the similarity to the reference image to a large extent. The project page is available at https://isotropic3d.github.io/. The code and models are available at https://github.com/pkunliu/Isotropic3D.

Score distillation of 2D diffusion models has proven to be a powerful mechanism to guide 3D optimization, for example enabling text-based 3D generation or single-view reconstruction. A common limitation of existing score distillation formulations, however, is that the outputs of the (mode-seeking) optimization are limited in diversity despite the underlying diffusion model being capable of generating diverse samples. In this work, inspired by the sampling process in denoising diffusion, we propose a score formulation that guides the optimization to follow generation paths defined by random initial seeds, thus ensuring diversity. We then present an approximation to adopt this formulation for scenarios where the optimization may not precisely follow the generation paths (e.g. a 3D representation whose renderings evolve in a co-dependent manner). We showcase the applications of our `Diverse Score Distillation' (DSD) formulation across tasks such as 2D optimization, text-based 3D inference, and single-view reconstruction. We also empirically validate DSD against prior score distillation formulations and show that it significantly improves sample diversity while preserving fidelity.

Recent advancements in text-to-3D generation technology have significantly advanced the conversion of textual descriptions into imaginative well-geometrical and finely textured 3D objects. Despite these developments, a prevalent limitation arises from the use of RGB data in diffusion or reconstruction models, which often results in models with inherent lighting and shadows effects that detract from their realism, thereby limiting their usability in applications that demand accurate relighting capabilities. To bridge this gap, we present UniDream, a text-to-3D generation framework by incorporating unified diffusion priors. Our approach consists of three main components: (1) a dual-phase training process to get albedo-normal aligned multi-view diffusion and reconstruction models, (2) a progressive generation procedure for geometry and albedo-textures based on Score Distillation Sample (SDS) using the trained reconstruction and diffusion models, and (3) an innovative application of SDS for finalizing PBR generation while keeping a fixed albedo based on Stable Diffusion model. Extensive evaluations demonstrate that UniDream surpasses existing methods in generating 3D objects with clearer albedo textures, smoother surfaces, enhanced realism, and superior relighting capabilities.

In this work, we introduce Unique3D, a novel image-to-3D framework for efficiently generating high-quality 3D meshes from single-view images, featuring state-of-the-art generation fidelity and strong generalizability. Previous methods based on Score Distillation Sampling (SDS) can produce diversified 3D results by distilling 3D knowledge from large 2D diffusion models, but they usually suffer from long per-case optimization time with inconsistent issues. Recent works address the problem and generate better 3D results either by finetuning a multi-view diffusion model or training a fast feed-forward model. However, they still lack intricate textures and complex geometries due to inconsistency and limited generated resolution. To simultaneously achieve high fidelity, consistency, and efficiency in single image-to-3D, we propose a novel framework Unique3D that includes a multi-view diffusion model with a corresponding normal diffusion model to generate multi-view images with their normal maps, a multi-level upscale process to progressively improve the resolution of generated orthographic multi-views, as well as an instant and consistent mesh reconstruction algorithm called ISOMER, which fully integrates the color and geometric priors into mesh results. Extensive experiments demonstrate that our Unique3D significantly outperforms other image-to-3D baselines in terms of geometric and textural details.

Text-to-3D generation has made remarkable progress recently, particularly with methods based on Score Distillation Sampling (SDS) that leverages pre-trained 2D diffusion models. While the usage of classifier-free guidance is well acknowledged to be crucial for successful optimization, it is considered an auxiliary trick rather than the most essential component. In this paper, we re-evaluate the role of classifier-free guidance in score distillation and discover a surprising finding: the guidance alone is enough for effective text-to-3D generation tasks. We name this method Classifier Score Distillation (CSD), which can be interpreted as using an implicit classification model for generation. This new perspective reveals new insights for understanding existing techniques. We validate the effectiveness of CSD across a variety of text-to-3D tasks including shape generation, texture synthesis, and shape editing, achieving results superior to those of state-of-the-art methods. Our project page is https://xinyu-andy.github.io/Classifier-Score-Distillation

Audio diffusion models can synthesize a wide variety of sounds. Existing models often operate on the latent domain with cascaded phase recovery modules to reconstruct waveform. This poses challenges when generating high-fidelity audio. In this paper, we propose EDMSound, a diffusion-based generative model in spectrogram domain under the framework of elucidated diffusion models (EDM). Combining with efficient deterministic sampler, we achieved similar Fr\'echet audio distance (FAD) score as top-ranked baseline with only 10 steps and reached state-of-the-art performance with 50 steps on the DCASE2023 foley sound generation benchmark. We also revealed a potential concern regarding diffusion based audio generation models that they tend to generate samples with high perceptual similarity to the data from training data. Project page: https://agentcooper2002.github.io/EDMSound/

Diffusion models have shown impressive results in text-to-image synthesis. Using massive datasets of captioned images, diffusion models learn to generate raster images of highly diverse objects and scenes. However, designers frequently use vector representations of images like Scalable Vector Graphics (SVGs) for digital icons or art. Vector graphics can be scaled to any size, and are compact. We show that a text-conditioned diffusion model trained on pixel representations of images can be used to generate SVG-exportable vector graphics. We do so without access to large datasets of captioned SVGs. By optimizing a differentiable vector graphics rasterizer, our method, VectorFusion, distills abstract semantic knowledge out of a pretrained diffusion model. Inspired by recent text-to-3D work, we learn an SVG consistent with a caption using Score Distillation Sampling. To accelerate generation and improve fidelity, VectorFusion also initializes from an image sample. Experiments show greater quality than prior work, and demonstrate a range of styles including pixel art and sketches. See our project webpage at https://ajayj.com/vectorfusion .

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

In the realm of text-to-3D generation, utilizing 2D diffusion models through score distillation sampling (SDS) frequently leads to issues such as blurred appearances and multi-faced geometry, primarily due to the intrinsically noisy nature of the SDS loss. Our analysis identifies the core of these challenges as the interaction among noise levels in the 2D diffusion process, the architecture of the diffusion network, and the 3D model representation. To overcome these limitations, we present StableDreamer, a methodology incorporating three advances. First, inspired by InstructNeRF2NeRF, we formalize the equivalence of the SDS generative prior and a simple supervised L2 reconstruction loss. This finding provides a novel tool to debug SDS, which we use to show the impact of time-annealing noise levels on reducing multi-faced geometries. Second, our analysis shows that while image-space diffusion contributes to geometric precision, latent-space diffusion is crucial for vivid color rendition. Based on this observation, StableDreamer introduces a two-stage training strategy that effectively combines these aspects, resulting in high-fidelity 3D models. Third, we adopt an anisotropic 3D Gaussians representation, replacing Neural Radiance Fields (NeRFs), to enhance the overall quality, reduce memory usage during training, and accelerate rendering speeds, and better capture semi-transparent objects. StableDreamer reduces multi-face geometries, generates fine details, and converges stably.

We present Condition-Aware Neural Network (CAN), a new method for adding control to image generative models. In parallel to prior conditional control methods, CAN controls the image generation process by dynamically manipulating the weight of the neural network. This is achieved by introducing a condition-aware weight generation module that generates conditional weight for convolution/linear layers based on the input condition. We test CAN on class-conditional image generation on ImageNet and text-to-image generation on COCO. CAN consistently delivers significant improvements for diffusion transformer models, including DiT and UViT. In particular, CAN combined with EfficientViT (CaT) achieves 2.78 FID on ImageNet 512x512, surpassing DiT-XL/2 while requiring 52x fewer MACs per sampling step.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

Diffusion models have shown remarkable performance in generation problems over various domains including images, videos, text, and audio. A practical bottleneck of diffusion models is their sampling speed, due to the repeated evaluation of score estimation networks during the inference. In this work, we propose a novel framework capable of adaptively allocating compute required for the score estimation, thereby reducing the overall sampling time of diffusion models. We observe that the amount of computation required for the score estimation may vary along the time step for which the score is estimated. Based on this observation, we propose an early-exiting scheme, where we skip the subset of parameters in the score estimation network during the inference, based on a time-dependent exit schedule. Using the diffusion models for image synthesis, we show that our method could significantly improve the sampling throughput of the diffusion models without compromising image quality. Furthermore, we also demonstrate that our method seamlessly integrates with various types of solvers for faster sampling, capitalizing on their compatibility to enhance overall efficiency. The source code and our experiments are available at https://github.com/taehong-moon/ee-diffusion

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by 25-75\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around 6-8times better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with 32times fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved question: which score do they actually learn? In principle, a diffusion model that matches the empirical score in the entire data space would simply reproduce the training data, failing to generate novel samples. Recent work addresses this question by arguing that diffusion models underfit the empirical score due to training-time inductive biases. In this work, we refine this perspective, introducing the notion of selective underfitting: instead of underfitting the score everywhere, better diffusion models more accurately approximate the score in certain regions of input space, while underfitting it in others. We characterize these regions and design empirical interventions to validate our perspective. Our results establish that selective underfitting is essential for understanding diffusion models, yielding new, testable insights into their generalization and generative performance.

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.

Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer from a coherence-quality tradeoff, where models with good generation quality lack generative coherence across modalities, and vice versa. We discuss the limitations underlying the unsatisfactory performance of existing methods, to motivate the need for a different approach. We propose a novel method that uses a set of independently trained, uni-modal, deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is fed to a masked diffusion model to enable generative modeling. We also introduce a new multi-time training method to learn the conditional score network for multi-modal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

Diffusion models have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose Score Augmentation (ScoreAug), a novel data augmentation framework specifically designed for diffusion models. Unlike conventional augmentation approaches that operate on clean data, ScoreAug applies transformations to noisy data, aligning with the inherent denoising mechanism of diffusion. Crucially, ScoreAug further requires the denoiser to predict the augmentation of the original target. This design establishes an equivariant learning objective, enabling the denoiser to learn scores across varied denoising spaces, thereby realizing what we term score augmentation. We also theoretically analyze the relationship between scores in different spaces under general transformations. In experiments, we extensively validate ScoreAug on multiple benchmarks including CIFAR-10, FFHQ, AFHQv2, and ImageNet, with results demonstrating significant performance improvements over baselines. Notably, ScoreAug effectively mitigates overfitting across diverse scenarios, such as varying data scales and model capacities, while exhibiting stable convergence properties. Another advantage of ScoreAug over standard data augmentation lies in its ability to circumvent data leakage issues under certain conditions. Furthermore, we show that ScoreAug can be synergistically combined with traditional data augmentation techniques to achieve additional performance gains.

A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION dataset.

Generative models, particularly diffusion models, have made significant success in data synthesis across various modalities, including images, videos, and 3D assets. However, current diffusion models are computationally intensive, often requiring numerous sampling steps that limit their practical application, especially in video generation. This work introduces a novel framework for diffusion distillation and distribution matching that dramatically reduces the number of inference steps while maintaining-and potentially improving-generation quality. Our approach focuses on distilling pre-trained diffusion models into a more efficient few-step generator, specifically targeting video generation. By leveraging a combination of video GAN loss and a novel 2D score distribution matching loss, we demonstrate the potential to generate high-quality video frames with substantially fewer sampling steps. To be specific, the proposed method incorporates a denoising GAN discriminator to distil from the real data and a pre-trained image diffusion model to enhance the frame quality and the prompt-following capabilities. Experimental results using AnimateDiff as the teacher model showcase the method's effectiveness, achieving superior performance in just four sampling steps compared to existing techniques.

Diffusion models have shown promising results for a wide range of generative tasks with continuous data, such as image and audio synthesis. However, little progress has been made on using diffusion models to generate discrete symbolic music because this new class of generative models are not well suited for discrete data while its iterative sampling process is computationally expensive. In this work, we propose a diffusion model combined with a Generative Adversarial Network, aiming to (i) alleviate one of the remaining challenges in algorithmic music generation which is the control of generation towards a target emotion, and (ii) mitigate the slow sampling drawback of diffusion models applied to symbolic music generation. We first used a trained Variational Autoencoder to obtain embeddings of a symbolic music dataset with emotion labels and then used those to train a diffusion model. Our results demonstrate the successful control of our diffusion model to generate symbolic music with a desired emotion. Our model achieves several orders of magnitude improvement in computational cost, requiring merely four time steps to denoise while the steps required by current state-of-the-art diffusion models for symbolic music generation is in the order of thousands.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

While diffusion models show promising results in image editing given a target prompt, achieving both prompt fidelity and background preservation remains difficult. Recent works have introduced score distillation techniques that leverage the rich generative prior of text-to-image diffusion models to solve this task without additional fine-tuning. However, these methods often struggle with tasks such as object insertion. Our investigation of these failures reveals significant variations in gradient magnitude and spatial distribution, making hyperparameter tuning highly input-specific or unsuccessful. To address this, we propose two simple yet effective modifications: attention-based spatial regularization and gradient filtering-normalization, both aimed at reducing these variations during gradient updates. Experimental results show our method outperforms state-of-the-art score distillation techniques in prompt fidelity, improving successful edits while preserving the background. Users also preferred our method over state-of-the-art techniques across three metrics, and by 58-64% overall.

Despite the potential of diffusion models in speech enhancement, their deployment in Acoustic Echo Cancellation (AEC) has been restricted. In this paper, we propose DI-AEC, pioneering a diffusion-based stochastic regeneration approach dedicated to AEC. Further, we propose FADI-AEC, fast score-based diffusion AEC framework to save computational demands, making it favorable for edge devices. It stands out by running the score model once per frame, achieving a significant surge in processing efficiency. Apart from that, we introduce a novel noise generation technique where far-end signals are utilized, incorporating both far-end and near-end signals to refine the score model's accuracy. We test our proposed method on the ICASSP2023 Microsoft deep echo cancellation challenge evaluation dataset, where our method outperforms some of the end-to-end methods and other diffusion based echo cancellation methods.

We introduce a film score generation framework to harmonize visual pixels and music melodies utilizing a latent diffusion model. Our framework processes film clips as input and generates music that aligns with a general theme while offering the capability to tailor outputs to a specific composition style. Our model directly produces music from video, utilizing a streamlined and efficient tuning mechanism on ControlNet. It also integrates a film encoder adept at understanding the film's semantic depth, emotional impact, and aesthetic appeal. Additionally, we introduce a novel, effective yet straightforward evaluation metric to evaluate the originality and recognizability of music within film scores. To fill this gap for film scores, we curate a comprehensive dataset of film videos and legendary original scores, injecting domain-specific knowledge into our data-driven generation model. Our model outperforms existing methodologies in creating film scores, capable of generating music that reflects the guidance of a maestro's style, thereby redefining the benchmark for automated film scores and laying a robust groundwork for future research in this domain. The code and generated samples are available at https://anonymous.4open.science/r/HPM.

A well-known limitation of existing molecular generative models is that the generated molecules highly resemble those in the training set. To generate truly novel molecules that may have even better properties for de novo drug discovery, more powerful exploration in the chemical space is necessary. To this end, we propose Molecular Out-Of-distribution Diffusion(MOOD), a score-based diffusion scheme that incorporates out-of-distribution (OOD) control in the generative stochastic differential equation (SDE) with simple control of a hyperparameter, thus requires no additional costs. Since some novel molecules may not meet the basic requirements of real-world drugs, MOOD performs conditional generation by utilizing the gradients from a property predictor that guides the reverse-time diffusion process to high-scoring regions according to target properties such as protein-ligand interactions, drug-likeness, and synthesizability. This allows MOOD to search for novel and meaningful molecules rather than generating unseen yet trivial ones. We experimentally validate that MOOD is able to explore the chemical space beyond the training distribution, generating molecules that outscore ones found with existing methods, and even the top 0.01% of the original training pool. Our code is available at https://github.com/SeulLee05/MOOD.

Optimization-based approaches, such as score distillation sampling (SDS), show promise in zero-shot 3D generation but suffer from low efficiency, primarily due to the high number of function evaluations (NFEs) required for each sample. In this paper, we introduce score-based iterative reconstruction (SIR), an efficient and general algorithm for 3D generation with a multi-view score-based diffusion model. Given the images produced by the diffusion model, SIR reduces NFEs by repeatedly optimizing 3D parameters, unlike the single optimization in SDS, mimicking the 3D reconstruction process. With other improvements including optimization in the pixel space, we present an efficient approach called MicroDreamer that generally applies to various 3D representations and 3D generation tasks. In particular, retaining a comparable performance, MicroDreamer is 5-20 times faster than SDS in generating neural radiance field and takes about 20 seconds to generate meshes from 3D Gaussian splitting on a single A100 GPU, halving the time of the fastest zero-shot baseline, DreamGaussian. Our code is available at https://github.com/ML-GSAI/MicroDreamer.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Developing generative models to create or conditionally create symbolic music presents unique challenges due to the combination of limited data availability and the need for high precision in note pitch. To address these challenges, we introduce an efficient Fine-Grained Guidance (FGG) approach within diffusion models. FGG guides the diffusion models to generate music that aligns more closely with the control and intent of expert composers, which is critical to improve the accuracy, listenability, and quality of generated music. This approach empowers diffusion models to excel in advanced applications such as improvisation, and interactive music creation. We derive theoretical characterizations for both the challenges in symbolic music generation and the effects of the FGG approach. We provide numerical experiments and subjective evaluation to demonstrate the effectiveness of our approach. We have published a demo page to showcase performances, as one of the first in the symbolic music literature's demo pages that enables real-time interactive generation.

Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples will have arbitrarily small errors in sampling from any continuous target distribution. We set up a unifying framework that debunks this belief. We demonstrate that broad classes of deep generative models, including variational autoencoders and generative adversarial networks, are not universal generators. Under the predominant case of Gaussian latent variables, these models can only generate concentrated samples that exhibit light tails. Using tools from concentration of measure and convex geometry, we give analogous results for more general log-concave and strongly log-concave latent variable distributions. We extend our results to diffusion models via a reduction argument. We use the Gromov--Levy inequality to give similar guarantees when the latent variables lie on manifolds with positive Ricci curvature. These results shed light on the limited capacity of common deep generative models to handle heavy tails. We illustrate the empirical relevance of our work with simulations and financial data.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which addresses both families of tasks simultaneously. We identify diffusion models, a state-of-the-art method for generative tasks, as a prime candidate. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high-fidelity, diverse, novel images. We find that the intermediate feature maps of the U-Net are diverse, discriminative feature representations. We propose a novel attention mechanism for pooling feature maps and further leverage this mechanism as DifFormer, a transformer feature fusion of features from different diffusion U-Net blocks and noise steps. We also develop DifFeed, a novel feedback mechanism tailored to diffusion. We find that diffusion models are better than GANs, and, with our fusion and feedback mechanisms, can compete with state-of-the-art unsupervised image representation learning methods for discriminative tasks - image classification with full and semi-supervision, transfer for fine-grained classification, object detection and segmentation, and semantic segmentation. Our project website (https://mgwillia.github.io/diffssl/) and code (https://github.com/soumik-kanad/diffssl) are available publicly.

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from x_t to x_{t-1}, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Diffusion-based generative models have achieved remarkable success in image generation. Their guidance formulation allows an external model to plug-and-play control the generation process for various tasks without finetuning the diffusion model. However, the direct use of publicly available off-the-shelf models for guidance fails due to their poor performance on noisy inputs. For that, the existing practice is to fine-tune the guidance models with labeled data corrupted with noises. In this paper, we argue that this practice has limitations in two aspects: (1) performing on inputs with extremely various noises is too hard for a single guidance model; (2) collecting labeled datasets hinders scaling up for various tasks. To tackle the limitations, we propose a novel strategy that leverages multiple experts where each expert is specialized in a particular noise range and guides the reverse process of the diffusion at its corresponding timesteps. However, as it is infeasible to manage multiple networks and utilize labeled data, we present a practical guidance framework termed Practical Plug-And-Play (PPAP), which leverages parameter-efficient fine-tuning and data-free knowledge transfer. We exhaustively conduct ImageNet class conditional generation experiments to show that our method can successfully guide diffusion with small trainable parameters and no labeled data. Finally, we show that image classifiers, depth estimators, and semantic segmentation models can guide publicly available GLIDE through our framework in a plug-and-play manner. Our code is available at https://github.com/riiid/PPAP.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Music scores are written representations of music and contain rich information about musical components. The visual information on music scores includes notes, rests, staff lines, clefs, dynamics, and articulations. This visual information in music scores contains more semantic information than audio and symbolic representations of music. Previous music score datasets have limited sizes and are mainly designed for optical music recognition (OMR). There is a lack of research on creating a large-scale benchmark dataset for music modeling and generation. In this work, we propose MusicScore, a large-scale music score dataset collected and processed from the International Music Score Library Project (IMSLP). MusicScore consists of image-text pairs, where the image is a page of a music score and the text is the metadata of the music. The metadata of MusicScore is extracted from the general information section of the IMSLP pages. The metadata includes rich information about the composer, instrument, piece style, and genre of the music pieces. MusicScore is curated into small, medium, and large scales of 400, 14k, and 200k image-text pairs with varying diversity, respectively. We build a score generation system based on a UNet diffusion model to generate visually readable music scores conditioned on text descriptions to benchmark the MusicScore dataset for music score generation. MusicScore is released to the public at https://huggingface.co/datasets/ZheqiDAI/MusicScore.

Recently, text-guided scalable vector graphics (SVGs) synthesis has shown promise in domains such as iconography and sketch. However, existing text-to-SVG generation methods lack editability and struggle with visual quality and result diversity. To address these limitations, we propose a novel text-guided vector graphics synthesis method called SVGDreamer. SVGDreamer incorporates a semantic-driven image vectorization (SIVE) process that enables the decomposition of synthesis into foreground objects and background, thereby enhancing editability. Specifically, the SIVE process introduce attention-based primitive control and an attention-mask loss function for effective control and manipulation of individual elements. Additionally, we propose a Vectorized Particle-based Score Distillation (VPSD) approach to tackle the challenges of color over-saturation, vector primitives over-smoothing, and limited result diversity in existing text-to-SVG generation methods. Furthermore, on the basis of VPSD, we introduce Reward Feedback Learning (ReFL) to accelerate VPSD convergence and improve aesthetic appeal. Extensive experiments have been conducted to validate the effectiveness of SVGDreamer, demonstrating its superiority over baseline methods in terms of editability, visual quality, and diversity.

Diffusion models have shown promising results in cross-modal generation tasks involving audio and music, such as text-to-sound and text-to-music generation. These text-controlled music generation models typically focus on generating music by capturing global musical attributes like genre and mood. However, music composition is a complex, multilayered task that often involves musical arrangement as an integral part of the process. This process involves composing each instrument to align with existing ones in terms of beat, dynamics, harmony, and melody, requiring greater precision and control over tracks than text prompts usually provide. In this work, we address these challenges by extending the MusicLDM, a latent diffusion model for music, into a multi-track generative model. By learning the joint probability of tracks sharing a context, our model is capable of generating music across several tracks that correspond well to each other, either conditionally or unconditionally. Additionally, our model is capable of arrangement generation, where the model can generate any subset of tracks given the others (e.g., generating a piano track complementing given bass and drum tracks). We compared our model with an existing multi-track generative model and demonstrated that our model achieves considerable improvements across objective metrics for both total and arrangement generation tasks.

Diffusion models trained with mean squared error loss tend to generate unrealistic samples. Current state-of-the-art models rely on classifier-free guidance to improve sample quality, yet its surprising effectiveness is not fully understood. In this paper, We show that the effectiveness of classifier-free guidance partly originates from it being a form of implicit perceptual guidance. As a result, we can directly incorporate perceptual loss in diffusion training to improve sample quality. Since the score matching objective used in diffusion training strongly resembles the denoising autoencoder objective used in unsupervised training of perceptual networks, the diffusion model itself is a perceptual network and can be used to generate meaningful perceptual loss. We propose a novel self-perceptual objective that results in diffusion models capable of generating more realistic samples. For conditional generation, our method only improves sample quality without entanglement with the conditional input and therefore does not sacrifice sample diversity. Our method can also improve sample quality for unconditional generation, which was not possible with classifier-free guidance before.

We propose an effective denoising diffusion model for generating high-resolution images (e.g., 1024times512), trained on small-size image patches (e.g., 64times64). We name our algorithm Patch-DM, in which a new feature collage strategy is designed to avoid the boundary artifact when synthesizing large-size images. Feature collage systematically crops and combines partial features of the neighboring patches to predict the features of a shifted image patch, allowing the seamless generation of the entire image due to the overlap in the patch feature space. Patch-DM produces high-quality image synthesis results on our newly collected dataset of nature images (1024times512), as well as on standard benchmarks of smaller sizes (256times256), including LSUN-Bedroom, LSUN-Church, and FFHQ. We compare our method with previous patch-based generation methods and achieve state-of-the-art FID scores on all four datasets. Further, Patch-DM also reduces memory complexity compared to the classic diffusion models.