提出ABC模型,实现任意时间点条件下的连续时空过程生成。
ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
- 用连续时空中非马尔可夫扩散桥建模过程,状态随真实时间演进。
- 生成起点为邻近历史状态,噪声随物理时间变化,动态更合理。
- 支持任意子集条件(如不规则采样或未来观测),适用于视频与天气预测。
在部分观测(如首尾帧)条件下生成连续时间、连续空间的随机过程(如视频、天气预报)是基础挑战。现有方法(如扩散模型)存在三大局限:(1) 噪声到数据的演化无法捕捉时间相近状态间的结构相似性,且低步数下积分不稳定;(2) 注入噪声对物理时间流逝不敏感,导致动态错误;(3) 忽视对任意状态子集的条件建模(如不规则采样时间点、未来观测)。本文提出ABC:基于连续时空非马尔可夫扩散桥的任意子集自回归模型。核心在于使用一个持续演化的随机微分方程(SDE),其时间变量与中间状态跟踪真实时间与过程状态。该设计具有三重优势:(1) 生成未来状态的起始点为邻近历史状态,而非无信息噪声;(2) 随机噪声注入量与物理时间间隔成比例,促进时间相邻状态间具物理合理性;(3) 通过路径空间上的测度变换推导出路径依赖的条件机制,支持对任意历史或未来状态子集的条件建模。为学习这些动态,我们推导了路径与时间依赖的去噪得分匹配扩展方法。实验表明,ABC在视频生成与天气预测等多个领域均优于现有方法。
原文摘要 · Abstract (English)
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.
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