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

arXiv cs.LG / 5/1/2026

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Key Points

The paper addresses conditional generation of continuous-time, continuous-space stochastic processes (such as videos and weather forecasts) from partial observations, highlighting limitations of existing diffusion-based methods.
It proposes “ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges,” which uses a single continuous-time SDE whose time parameter and intermediate states align with real physical time and process states.
The method is designed so that generation starts from an already-relevant previous state (not uninformative noise) and scales injected randomness with the physical time elapsed to improve physically plausible dynamics.
Using changes-of-measure on path space, ABC enables path-dependent conditioning on arbitrary subsets of the state history or future, and it trains via a path- and time-dependent variant of denoising score matching.
Experiments report that ABC outperforms competing approaches across domains including video generation and weather forecasting.

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.