ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
cs.LG, cs.AI
Submitted: 2026-04-30
Updated: 2026-08-28
Code: https://github.com/gabeguo/abc_diffusion
Project page: https://abc-diffusion.github.io
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
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.
Sources
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- Fractional Diffusion Bridge Models
- Non-Denoising Forward-Time Diffusions
- Meta Flow Maps enable scalable reward alignment
- Score-Based Generative Modeling through Stochastic Differential Equations
- Momentum Multi-Marginal Schr\"odinger Bridge Matching
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