DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

Equivariant Energy-Guided SDE for Inverse Molecular Design

Inverse molecular design is critical in material science and drug discovery, where the generated molecules should satisfy certain desirable properties. In this paper, we propose equivariant energy-guided stochastic differential equations (EEGSDE), a flexible framework for controllable 3D molecule generation under the guidance of an energy function in diffusion models. Formally, we show that EEGSDE naturally exploits the geometric symmetry in 3D molecular conformation, as long as the energy function is invariant to orthogonal transformations. Empirically, under the guidance of designed energy functions, EEGSDE significantly improves the baseline on QM9, in inverse molecular design targeted to quantum properties and molecular structures. Furthermore, EEGSDE is able to generate molecules with multiple target properties by combining the corresponding energy functions linearly.

All are Worth Words: a ViT Backbone for Score-based Diffusion Models

Vision transformers (ViT) have shown promise in various vision tasks including low-level ones while the U-Net remains dominant in score-based diffusion models. In this paper, we perform a systematical empirical study on the ViT-based architectures in diffusion models. Our results suggest that adding extra long skip connections (like the U-Net) to ViT is crucial to diffusion models. The new ViT architecture, together with other improvements, is referred to as U-ViT. On several popular visual datasets, U-ViT achieves competitive generation results to SOTA U-Net while requiring comparable amount of parameters and computation if not less.

Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Models

Deep generative models (DGMs) are data-eager. Essentially, it is because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the \emph{bias-variance dilemma}, we propose \emph{regularized deep generative model} (Reg-DGM), which leverages a nontransferable pre-trained model to reduce the variance of generative modeling with limited data. Formally, Reg-DGM optimizes a weighted sum of a certain divergence between the data distribution and the DGM and the expectation of an energy function defined by the pre-trained model w.r.t. the DGM. Theoretically, we characterize the existence and uniqueness of the global minimum of Reg-DGM in the nonparametric setting and rigorously prove the statistical benefits of Reg-DGM w.r.t. the mean squared error and the expected risk in a simple yet representative Gaussian-fitting example. Empirically, it is quite flexible to specify the DGM and the pre-trained model in Reg-DGM. In particular, with a ResNet-18 classifier pre-trained on ImageNet and a data-dependent energy function, Reg-DGM consistently improves the generation performance of strong DGMs including StyleGAN2 and ADA on several benchmarks with limited data and achieves competitive results to the state-of-the-art methods.

EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations

Score-based diffusion generative models (SDGMs) have achieved the SOTA FID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domainspecific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics. EGSDE not only consistently outperforms existing SDGMs-based methods in almost all settings but also achieves the SOTA realism results (e.g., FID of 65.82 in Cat to Dog and FID of 59.75 in Wild to Dog on AFHQ) without harming the faithful performance.

Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE ("score-based diffusion ODE") for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.

Fast Lossless Neural Compression with Integer-Only Discrete Flows

By applying entropy codecs with learned data distributions, neural compressors have significantly outperformed traditional codecs in terms of compression ratio. However, the high inference latency of neural networks hinders the deployment of neural compressors in practical applications. In this work, we propose Integer-only Discrete Flows (IODF), an efficient neural compressor with integer-only arithmetic. Our work is built upon integer discrete flows, which consists of invertible transformations between discrete random variables. We propose efficient invertible transformations with integer-only arithmetic based on 8-bit quantization. Our invertible transformation is equipped with learnable binary gates to remove redundant filters during inference. We deploy IODF with TensorRT on GPUs, achieving 10x inference speedup compared to the fastest existing neural compressors, while retaining the high compression rates on ImageNet32 and ImageNet64.

Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models

Diffusion probabilistic models (DPMs) are a class of powerful deep generative models (DGMs). Despite their success, the iterative generation process over the full timesteps is much less efficient than other DGMs such as GANs. Thus, the generation performance on a subset of timesteps is crucial, which is greatly influenced by the covariance design in DPMs. In this work, we consider diagonal and full covariances to improve the expressive power of DPMs. We derive the optimal result for such covariances, and then correct it when the mean of DPMs is imperfect. Both the optimal and the corrected ones can be decomposed into terms of conditional expectations over functions of noise. Building upon it, we propose to estimate the optimal covariance and its correction given imperfect mean by learning these conditional expectations. Our method can be applied to DPMs with both discrete and continuous timesteps. We consider the diagonal covariance in our implementation for computational efficiency. For an efficient practical implementation, we adopt a parameter sharing scheme and a two-stage training process. Empirically, our method outperforms a wide variety of covariance design on likelihood results, and improves the sample quality especially on a small number of timesteps.

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a $4\sim 16\times$ speedup compared with previous state-of-the-art training-free samplers on various datasets.