Abstract
Diffusion models are an important tool for generative modelling, serving as effective priors in applications such as imaging and protein design. A key challenge in applying diffusion models for downstream tasks is efficiently sampling from resulting posterior distributions, which can be addressed using Doob's -transform. This work introduces a self-supervised algorithm for fine-tuning diffusion models by learning the optimal control, enabling amortised conditional sampling. Our method iteratively refines the control using a synthetic dataset resampled with path-based importance weights. We demonstrate the effectiveness of this framework on class-conditional sampling, inverse problems and reward fine-tuning for text-to-image diffusion models.