SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models

2023-09-10

Neural Information Processing Systems

AI Summary

Diffusion probabilistic models (DPMs) require solving computationally expensive diffusion stochastic differential equations (SDEs) or ordinary differential equations (ODEs) during sampling; existing acceleration methods predominantly target deterministic ODE solvers, struggling to balance generation fidelity and diversity. This work proposes the first stochastic Adams linear multistep solver tailored for diffusion SDEs, jointly optimizing fidelity and diversity with minimal function evaluations (20–50 NFEs) via variance-controlled SDE modeling, a novel stochastic integrator design, and NFE-aware scheduling. Its core innovation lies in the first integration of the stochastic Adams method with the linear multistep framework for SDE solving. On benchmarks including CIFAR-10 and CelebA-HQ, our method achieves state-of-the-art FID scores in only 4–8 sampling steps—substantially outperforming both existing deterministic and stochastic samplers.

Abstract

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

Problem

• Fast sampling from Diffusion Probabilistic Models
• Improving stochastic sampling for diverse data generation
• Enhancing efficiency of solving diffusion SDEs

Innovation

• Stochastic Adams method for diffusion SDE
• Variance-controlled diffusion SDE analysis
• Linear multi-step SDE solver optimization