An effective potential for generative modelling with active matter

Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications such as artificial image synthesis. Here, I show how a generative diffusion model can be implemented based on an underlying active particle process with finite correlation time. In contrast to previous approaches that use a score function acting on the velocity coordinate of the active particle, time reversal is here achieved by imposing an effective time-dependent potential on the position coordinate only. The effective potential is valid to first order in the persistence time and leads to a force field that is fully determined by the standard score function and its derivatives up to 2nd order. Numerical experiments for artificial data distributions confirm the validity of the effective potential.