**Abstract:**

Diffusion models based on stochastic differential equations (SDEs) gradually perturb a data distribution p(x) over time by adding noise to it. A neural network is trained to approximate the score ∇xlogpt(x) at time t, which can be used to reverse the corruption process. In this paper, we focus on learning the score field that is associated with the time evolution according to a physics operator in the presence of natural non-deterministic physical processes like diffusion. A decisive difference to previous methods is that the SDE underlying our approach transforms the state of a physical system to another state at a later time. For that purpose, we replace the drift of the underlying SDE formulation with a differentiable simulator or a neural network approximation of the physics. We propose different training strategies based on the so-called probability flow ODE to fit a training set of simulation trajectories and discuss their relation to the score matching objective. For inference, we sample plausible trajectories that evolve towards a given end state using the reverse-time SDE and demonstrate the competitiveness of our approach for different challenging inverse problems.

**Paper link:** https://arxiv.org/abs/2301.10250

**ZOOM LINK: **https://uci.zoom.us/j/97010614727