Improved Order Analysis and Design of Exponential Integrator for Diffusion Models Sampling

• URL: http://arxiv.org/abs/2308.02157v1
• Date: Fri, 4 Aug 2023 06:30:40 GMT
• Title: Improved Order Analysis and Design of Exponential Integrator for Diffusion Models Sampling
• Authors: Qinsheng Zhang and Jiaming Song and Yongxin Chen
• Abstract summary: Exponential solvers have gained prominence by demonstrating state-of-the-art performance. Existing high-order EI-based sampling algorithms rely on degenerate EI solvers. We propose refined EI solvers that fulfill all the order conditions.
• Score: 36.50606582918392
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) $=9$, results in a reduction of numerical defects by $25.2\%$ and FID improvement of $25.4\%$ (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.

Related papers

• Accelerating Diffusion Sampling with Optimized Time Steps [69.21208434350567]
  Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis. Their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in high-order numerical ODE solvers for DPMs have enabled the generation of high-quality images with much fewer sampling steps.
  arXiv  Detail & Related papers  (2024-02-27T10:13:30Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models [0.49478969093606673]
  A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. Despite being quick, such solvers do not usually reach the optimal quality achieved by available slow SDE solvers. Our goal is to propose SDE solvers that reach optimal quality without requiring several hundreds or thousands of NFEs to achieve that goal.
  arXiv  Detail & Related papers  (2023-05-23T17:19:54Z)
• Conditional Denoising Diffusion for Sequential Recommendation [62.127862728308045]
  Two prominent generative models, Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs) GANs suffer from unstable optimization, while VAEs are prone to posterior collapse and over-smoothed generations. We present a conditional denoising diffusion model, which includes a sequence encoder, a cross-attentive denoising decoder, and a step-wise diffuser.
  arXiv  Detail & Related papers  (2023-04-22T15:32:59Z)
• On Accelerating Diffusion-Based Sampling Process via Improved Integration Approximation [12.882586878998579]
  A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE) We consider accelerating several popular ODE-based sampling processes by optimizing certain coefficients via improved integration approximation (IIA) We show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-r than the original counterparts.
  arXiv  Detail & Related papers  (2023-04-22T06:06:28Z)
• Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning [45.78238792836363]
  We present a single-loop algorithm named SLEDGE (Single-Loop-E Gradient Estimator) for periodic convergence. Unlike existing methods, SLEDGE has the advantage of versatility; (ii) second-order optimal, (ii) in the PL region, and (iii) smaller complexity under less of data.
  arXiv  Detail & Related papers  (2022-09-01T11:05:26Z)
• DR-DSGD: A Distributionally Robust Decentralized Learning Algorithm over Graphs [54.08445874064361]
  We propose to solve a regularized distributionally robust learning problem in the decentralized setting. By adding a Kullback-Liebler regularization function to the robust min-max optimization problem, the learning problem can be reduced to a modified robust problem. We show that our proposed algorithm can improve the worst distribution test accuracy by up to $10%$.
  arXiv  Detail & Related papers  (2022-08-29T18:01:42Z)
• Sinkhorn Distributionally Robust Optimization [15.194516549163245]
  We derive convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. Compared with Wasserstein DRO, our proposed approach offers enhanced computational tractability for a broader class of loss functions.
  arXiv  Detail & Related papers  (2021-09-24T12:40:48Z)
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization [85.84019017587477]
  Distributionally robust supervised learning is emerging as a key paradigm for building reliable machine learning systems for real-world applications. Existing algorithms for solving Wasserstein DRSL involve solving complex subproblems or fail to make use of gradients. We revisit Wasserstein DRSL through the lens of min-max optimization and derive scalable and efficiently implementable extra-gradient algorithms.
  arXiv  Detail & Related papers  (2021-04-27T16:56:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.