Diffusion Timestep Scheduling

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers, the broader sampling design problem, specifically solver selection and scheduling, remains largely governed by static heuristics. We propose SDM, a principled, training-free sampling framework that adapts both the numerical solver and the timestep schedule to the intrinsic properties of the diffusion trajectory. By analyzing the PF-ODE dynamics, we show that velocity variation is small in high-noise stages and increases near the data manifold, identifying intervals where solver order is most consequential. In parallel, we introduce an offline-calibrated adaptive scheduling method that explicitly controls the local Wasserstein discretization error and projects the calibrated trajectory to a prescribed NFE budget. We further extend the formulation to a mixed-transition Wasserstein error bound, providing a unified error-propagation view of adaptive scheduling and solver selection within the overall SDM framework. Across standard benchmarks, with extensions to modern ODE samplers, high-resolution synthesis, and text-to-image generation, SDM achieves improved sample quality compared to baseline methods, attaining an FID of 1.93 on CIFAR-10, 2.41 on FFHQ, and 1.98 on AFHQv2, with a reduced number of function evaluations compared to existing samplers. Our code is available at https://github.com/aiimaginglab/sdm.

Uniform Discrete Diffusion Models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain underexplored. In this work, we bridge this gap by analyzing the reverse process dynamics through the lens of thermodynamic entropy production and dynamical activity. We use a variational expression of the discrete Wasserstein distance to characterize the dynamics of the generation process. Leveraging these insights, we first introduce the Entropic Discrete Schedule (EDS), which aligns with entropy production, and later construct the Wasserstein Discrete Schedule (WDS), which combines entropy production and dynamical activity to act as a geometric cost. Our experimental results on language modeling show that WDS provide the same results as uniform while using up to half of the computations on the MBPP benchmark. The code is available at https://github.com/AlbertoForesti/impscheds.

We consider time discretization for score-based diffusion models to generate samples from a learned reverse-time dynamic on a finite grid. Uniform and hand-crafted grids can be suboptimal given a budget on the number of time steps. We introduce Adaptive Reparameterized Time (ART), which controls the clock speed of a reparameterized time variable to redistribute computation along the sampling trajectory while preserving the terminal time, with the objective of minimizing the aggregate Euler discretization error. We derive a randomized companion ART-RL that recasts ART as a continuous-time reinforcement learning problem with Gaussian policies, and prove a two-directional bridge between the two: the deterministic ART optimum lifts to an optimal Gaussian policy, and conversely any optimal Gaussian policy must recover the ART control through its mean. This bridge turns continuous-time actor--critic learning into a principled, rather than heuristic, route to the deterministic timestep optimum. Within the official EDM pipeline, ART-RL improves FID on CIFAR--10 across a wide range of budgets; after one-time offline training, the distilled deterministic schedule transfers without retraining to AFHQv2, FFHQ, and ImageNet at no extra inference cost.

Diffusion models have been widely adopted as a powerful generative framework across numerous scientific domains, yet their inherently iterative sampling process remains a significant computational bottleneck. While this is typically mitigated by reducing the number of reverse diffusion steps, sample quality becomes highly sensitive to the chosen noise schedule, i.e. the manner in which noise is introduced and the signal is reduced at each step. Although prior work has improved on the original variance-preserving and variance-exploding schedules, these approaches passively adjust the total variance, without direct independent control over it. In this work, we propose a novel total-variance/signal-to-noise-ratio disentangled (TV/SNR) framework, where TV and SNR can be controlled independently. Our approach reveals that schedules with exponentially exploding TV can be consistently improved by adopting a constant TV schedule while preserving the underlying SNR schedule. Furthermore, we demonstrate that generalizing the SNR schedule of optimal transport flow matching significantly enhances generation efficiency. Crucially, these gains remain consistent across various reverse diffusion solvers and reduce the search space to two independent and interpretable parameters, enabling fast and robust sampling for complex scientific applications, such as molecular structure generation.