ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space

TL;DR

This paper introduces ABC, a novel continuous-time, continuous-space stochastic process model that improves conditioned generation by modeling with a single SDE, enabling better structural similarity, dynamic scaling, and arbitrary subset conditioning.

Contribution

The paper proposes a new non-Markovian diffusion bridge approach with a single SDE that tracks real time and states, allowing flexible conditioning and more realistic dynamics.

Findings

ABC outperforms existing methods in video generation tasks.

ABC demonstrates superior weather forecasting accuracy.

The model effectively handles arbitrary subset conditioning.

Abstract

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.