Score-Optimal Diffusion Schedules

Abstract: Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data distribution by incrementally injecting noise into the data. To numerically simulate the sampling process, a discretisation schedule from the reference back towards clean data must be chosen. An appropriate discretisation schedule is crucial to obtain high quality samples. However, beyond hand crafted heuristics, a general method for choosing this schedule remains elusive. This paper presents a novel algorithm for adaptively selecting an optimal discretisation schedule with respect to a cost that we derive. Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training. We find that our learned schedule recovers performant schedules previously only discovered through manual search and obtains competitive FID scores on image datasets.