arXiv Machine Learning
Oct 5

Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling

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.

By Ella Kemperman, Luca Ambrogioni
arXiv AI
Sep 3

GeoSPRINT: Geometric Redundancy-Aware Step Pruning for Inference in Diffusion Trajectories

GeoSPRINT is a training‑free framework that constructs non‑uniform sampling schedules for diffusion model inference by detecting geometrically redundant steps in denoising trajectories. It uses a hyperplanarity test in latent space, implemented via QR factorization, to allocate more steps to high‑curvature regions, and introduces the trajectory projection score α_traj as a model‑free diagnostic for flow quality. Across CIFAR‑10, LSUN Church, and Stable Diffusion v1.5, GeoSPRINT consistently outperforms uniform DDIM schedules at matched NFE budgets, improving FID scores by up to 1.93 points.

By Arpita Joshi
arXiv Computation and Language
Aug 28

Forward-Free Diffusion Language Models with BPTT-Free Looped Refinement

Forward-Free Diffusion Language Models with BPTT-Free Looped Refinement (FReDA) removes the need for a hand‑designed forward process in diffusion language modeling by treating model‑generated drafts as implicit intermediate states and refining them recursively. The approach detaches earlier refinement passes, backpropagating only through the final pass, and supports both self‑refinement and Best‑of‑N candidate selection. In sub‑8B experiments, FReDA‑4B surpasses larger diffusion baselines on reasoning and coding tasks, achieving up to 15% absolute gains and a 1.5‑1.8× speedup while scaling well with additional refinement steps.

By Haotian Sun, Rushi Qiang, Yuqian Zheng, Bo Dai