Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Models

TL;DR

This paper presents a novel method combining particle filtering and diffusion models to generate realistic, smoothed trajectories from sparse observations, applicable to diverse dynamical systems.

Contribution

It introduces a new approach that integrates conditional particle filtering with diffusion models for trajectory generation and approximation of smoothing distributions.

Findings

Effective in time-series generation and interpolation

Applicable to vehicle tracking and single-cell RNA data

Provides high-quality, constrained trajectory samples

Abstract

Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary machine learning models, such as diffusion models. We introduce a method that integrates conditional particle filtering with ancestral sampling and diffusion models, enabling the generation of realistic trajectories that align with observed data. Our approach uses a smoother based on iterating a conditional particle filter with ancestral sampling to first generate plausible trajectories matching observed marginals, and learns the corresponding diffusion model. This approach provides both a generative method for high-quality, smoothed trajectories under complex constraints, and an efficient approximation of the particle smoothing distribution for classical tracking problems. We demonstrate the approach in time-series generation and interpolation tasks, including vehicle tracking and single-cell RNA sequencing data.