  We propose to solve inverse problems involving the temporal evolution of
physics systems by leveraging recent advances from diffusion models. Our method
moves the system's current state backward in time step by step by combining an
approximate inverse physics simulator and a learned correction function. A
central insight of our work is that training the learned correction with a
single-step loss is equivalent to a score matching objective, while recursively
predicting longer parts of the trajectory during training relates to maximum
likelihood training of a corresponding probability flow. We highlight the
advantages of our algorithm compared to standard denoising score matching and
implicit score matching, as well as fully learned baselines for a wide range of
inverse physics problems. The resulting inverse solver has excellent accuracy
and temporal stability and, in contrast to other learned inverse solvers,
allows for sampling the posterior of the solutions.
