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Poster
in
Workshop: Machine Learning and the Physical Sciences

Score Matching via Differentiable Physics

Benjamin Holzschuh · Simona Vegetti · Nils Thuerey


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. At the core of our method, we optimize the so-called probability flow ODE to fit a training set of simulation trajectories inside an ODE solver and solve the reverse-time SDE for inference to sample plausible trajectories that evolve towards a given end state.

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