Causal Score Conditioning for Multi-Resolution Latent Systems

Xuechun Li, Shan Gao, Susu Xu

Keywords: Causal Score Conditioning, Variational causal inference, Probabilistic graphical models, Multi-resolution observations, Score-based diffusion models

Abstract: Complex causal systems with interdependent variables require inference from heterogeneous observations that vary in spatial resolution, temporal frequency, and noise characteristics due to data acquisition constraints. Existing multi-modal fusion approaches assume uniform data quality or complete observability -- assumptions often violated in real-world applications. Current methods face three limitations: they treat causally-related variables independently, failing to exploit causal relationships; they cannot integrate multi-resolution observations effectively; and they lack theoretical frameworks for cascaded approximation errors. We introduce the Score-based Variational Graphical Diffusion Model (SVGDM), which integrates score-based diffusion within causal graphical structures for inference under heterogeneous incomplete observations. SVGDM introduces causal score decomposition enabling information propagation across causally-connected variables while preserving original observation characteristics. Diffusion provides a natural way to model scale-dependent sensing noise, which is common in remote-sensing, climate, and physical measurement systems, while the causal graph encodes well-established mechanistic dependencies between latent processes. We provide theoretical analysis and demonstrate superior performance on both synthetic and real-world datasets compared to relevant baselines.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 11905