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. Here, I show how a generative diffusion model can be implemented based on an underlying active particle process with finite correlation time. Time reversal is achieved by imposing an effective time-dependent potential on the position coordinate, which can be readily implemented in simulations and experiments to generate new synthetic data samples driven by active fluctuations. 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, which opens up new avenues to exploit fluctuations in active and living systems for generative AI purposes.