SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models

2023/05/23 by Martin Gonzalez, Gonzalez, Martin, Nelson Fernández +9 · 6 citations
Computer Science · Physics and Astronomy · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #I.2.6 #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2305.14267

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is obtained by solving differential equations (DE) defined by the learnt model, a process which has shown to be prohibitively slow. Numerous efforts on speeding-up this process have consisted on crafting powerful ODE solvers. 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. We propose Stochastic Explicit Exponential Derivative-free Solvers (SEEDS), improving and generalizing Exponential Integrator approaches to the stochastic case on several frameworks. After carefully analyzing the formulation of exact solutions of diffusion SDEs, we craft SEEDS to analytically compute the linear part of such solutions. Inspired by the Exponential Time-Differencing method, SEEDS use a novel treatment of the stochastic components of solutions, enabling the analytical computation of their variance, and contains high-order terms allowing to reach optimal quality sampling ∼3-5× faster than previous SDE methods. We validate our approach on several image generation benchmarks, showing that SEEDS outperform or are competitive with previous SDE solvers. Contrary to the latter, SEEDS are derivative and training free, and we fully prove strong convergence guarantees for them.

Citations

• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• Denoising Diffusion Probabilistic Models
• Diffusion Models Beat GANs on Image Synthesis
• Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models
• Fast Sampling of Diffusion Models with Exponential Integrator
• Pseudo Numerical Methods for Diffusion Models on Manifolds
• Diffusion Models for Adversarial Purification
• Elucidating the Design Space of Diffusion-Based Generative Models
• SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations
• DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models
• gDDIM: Generalized denoising diffusion implicit models
• Better Diffusion Models Further Improve Adversarial Training
• Restart Sampling for Improving Generative Processes

Cited by

• Hierarchical Schedule Optimization for Fast and Robust Diffusion Model Sampling
• Sublinear iterations can suffice even for DDPMs
• Deep Neural Networks Inspired by Differential Equations
• EVODiff: Entropy-aware Variance Optimized Diffusion Inference
• DiffusionNFT: Online Diffusion Reinforcement with Forward Process
• A Selective Review of Modern Stochastic Modeling: SDE/SPDE Numerics, Data-Driven Identification, and Generative Methods with Applications in Biomathematics

Related

• Adaptive Stochastic Coefficients for Accelerating Diffusion Sampling
• DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps
• Fast Sampling of Diffusion Models with Exponential Integrator
• Elucidating the solution space of extended reverse-time SDE for diffusion models
• SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models