Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling
Read the original on arXiv Machine Learning →The paper introduces adaptive second‑order solvers for diffusion models, employing a proportional‑integral (PI) step‑size controller based on a diffusion noise‑normalised error estimator. Unlike existing adaptive methods that react only to the current error, the PI solver incorporates past error information, producing smoother step adaptations. The authors also demonstrate that per‑sample trajectories share structure, allowing aggregation into a fixed schedule that largely preserves adaptive benefits. Experiments on natural‑image and language datasets show that the fixed schedule outperforms the commonly used EDM schedule for image sampling with the stochastic Heun sampler, and that the PI adaptive solver achieves lower FID than most baselines, though it does not surpass the EDM‑churn sampler at low neural‑network‑evaluation counts. In language diffusion, the PI solver improves perplexity over EDM and entropy schedules at low‑to‑medium NFE, albeit with reduced token entropy. The study concludes that per‑sample adaptivity is highly beneficial for simple 1D toy problems but only marginally useful for image and language data, where an average schedule can sometimes outperform the PI‑adaptive approach.
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