Diffusion Differentiable Resampling

This paper is concerned with differentiable resampling in the context of sequential Monte Carlo (e.g., particle filtering). Drawing on reparametrisation, we propose a new resampling method that is informative and instantly differentiable, based on a training-free diffusion model surrogate. We theoretically prove that our diffusion resampling method provides a consistent resampling distribution, and we show empirically that it outperforms the state-of-the-art differentiable resampling methods on multiple filtering and parameter estimation benchmarks. Finally, we show that it achieves competitive end-to-end performance when used in learning a complex dynamics-decoder model with high-dimensional image observations.

Learning dynamical models (e.g., fluid dynamics, weather forecasting, and vision tracking) is an important problem across many scientific disciplines. To enable neural-network-based learning from data, one often needs to differentiate through a loss function defined by maximum likelihood estimation. However, such loss functions typically involve discrete randomness, breaking the differentiability. This paper provides a novel reparametrisation technique of the discrete randomness and guarantees full differentiability and statistical consistency, at low computatonal cost, powered by a diffusion model surrogate.