Is Monotonic Sampling Necessary in Diffusion Models?

TL;DR

This study investigates whether the common assumption of monotonic noise schedules in diffusion models is necessary, finding that nonmonotonic schedules do not outperform monotonic ones across various models and configurations.

Contribution

The paper introduces structured nonmonotonic schedules and the Schedule Sensitivity Coefficient to evaluate the importance of monotonicity in diffusion model sampling.

Findings

Nonmonotonic schedules do not improve over monotonic baselines in tested configurations.

The penalty for nonmonotonicity varies significantly across different architectures.

The Schedule Sensitivity Coefficient correlates with the model's convergence to the Bayes-optimal denoiser.

Abstract

Diffusion models generate samples by iteratively denoising a Gaussian prior, traversing a sequence of noise levels that, in every published sampler, decreases monotonically. Six years of intensive work has refined nearly every aspect of this recipe, including the corruption operator, the training objective, the schedule shape, the architecture, and the ODE solver. Yet the assumption of monotonicity itself has never been systematically tested. Here we ask whether monotonic sampling is load-bearing or merely conventional. We design four families of structured nonmonotonic schedules and apply them to three architecturally distinct generative models, DDPM, EDM, and Flow Matching, across NFE budgets ranging from 10 to 200 function evaluations, plus a 42-cell hyperparameter ablation, on CIFAR-10. Across all 90 tested configurations, no tested nonmonotonic schedule improves on the monotonic baseline. The magnitude of the penalty, however, spans nearly three orders of magnitude: persistent and substantial in DDPM, intermediate in Flow Matching, and indistinguishable from zero in EDM. We show that this variation is not noise but a structural property of each trained denoiser, and we formalize it as the Schedule Sensitivity Coefficient, a cheap, architecture-agnostic diagnostic that provides evidence of non-convergence to the Bayes-optimal denoiser at the critical noise level. Our findings justify the field's tacit reliance on monotonic schedules and supply a new probe of diffusion model quality complementary to sample-quality metrics such as Frechet Inception Distance.