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

Martin Gonzalez, Elies Gherbi, Hatem Hajri, Nader Masmoudi, Thuy Tran, Nelson Fernandez

Publication date: 23 May 2023

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. In this work, we propose Stochastic 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 uses 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

s i m 3

-

5 i m e s

faster than previous SDE methods. We validate our approach on several image generation benchmarks, showing that SEEDS outperforms or is competitive with previous SDE solvers. Contrary to the latter, SEEDS are derivative and training free, and we fully prove strong convergence guarantees for them.

Has companion code repository: https://github.com/nfsrules/seeds

This page was built for publication: SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6437700)