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

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion theory and design space · 0 citations (OpenAlex)

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Proposes ABC, a single continual SDE whose time tracks physical time, trained via a path- and time-dependent denoising score matching loss, to generate continuous-time any-subset conditioned stochastic processes such as videos and weather.

Problem

Generating continuous-time, continuous-space stochastic processes (videos, weather) conditioned on arbitrary subsets of observed states (irregular or future observations) is hard; existing noise-to-data diffusion and fixed-volatility diffusion bridges ignore physical time and cannot condition flexib

Approach

Model the process as one non-Markovian SDE obtained by a Doob h-transform of an OU base process, whose time variable equals physical time, with volatility scaled to elapsed time; the drift is a path- and time-dependent score learned by a generalized denoising score matching loss and parameterized by a cross-attention transformer over any observed subset of the history and future.

Key results

• On SEVIR VIL full test set, ABC non-causal achieves MAE 18.228 and RMSE 34.849 versus 35.698 MAE for noise-to-data diffusion and 55.196 MAE for conditional diffusion bridge.
• On Sky-Timelapse non-causal FVD (32 frames, pin_every=4, 500 steps), ABC no-BB reaches 58.1 versus best conditional bridge 72.7 and noise-to-data at 211.8 or higher.
• On CelebV-HQ non-causal FVD (32 frames, pin_every=4, 500 steps), ABC no-BB reaches 32.6, versus 181.7 for the best conditional bridge and 337.5 or higher for noise-to-data.

Surprising findings

• Conditional diffusion bridges with some fixed volatility can win on FVD but are not competitive on FID, indicating flickering videos that FVD underweights.
• Noise-to-data diffusion is far worse than all other methods on FVD across settings, especially at low step counts.

Limitations

• Transformer attends to the full history, which is not efficient for long sequences; SSMs suggested as future work.
• Sampling uses only a plain SDE; the paper notes hybrid ODE-SDE sampling is left for future work.
• Observation constraints at future times require approximation with small-variance Gaussians rather than exact Dirac conditioning.

Experimental setup

Datasets: CelebV-HQ Sky Timelapse SEVIR VIL

Benchmarks: Sky Timelapse CelebV-HQ SEVIR VIL

Metrics: FVD FID MAE RMSE CSI POD FAR Bias

Baselines: DDBM (conditional diffusion bridge) PFI (probabilistic forecasting with stochastic interpolants) SMLD / DDPM noise-to-data diffusion

Builds on: DDBM denoising diffusion models stochastic interpolants any-subset autoregressive models DiT

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