ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion

Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce—exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach—directly mapping exogenous inputs to targets—can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion—training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://github.com/YingdaFan/ZeroDiff-ICML2026.

Most of the world's rivers have no streamflow gauges. Most of its land has no methane sensors. Yet floods, droughts, and greenhouse gas emissions don't pause for the gaps in our monitoring networks. While indirect data like weather and satellite imagery are broadly available, the direct measurements we most need—streamflow, water temperature, solar radiation, atmospheric methane—exist at only a small subset of locations worldwide. So can a machine learning model trained where measurements exist reconstruct what's happening where they don't? The catch is this: without any target signal at the new location, the model has to commit to a single direct mapping from indirect data to target—and once it's trained, it has no way to know when it's wrong. That's why such predictions tend to be smooth and timid, underestimating the very floods, heatwaves, and emission spikes that matter most. ZeroDiff takes a different route. It first builds a rough sketch of the target from indirect data, then uses a diffusion-based calibration process—trained where measurements exist—to learn how to correct its own mistakes. In short, ZeroDiff doesn't just guess; it learns how to fix its guesses. Across four real-world datasets—river flow, solar energy, water temperature, and methane emissions—ZeroDiff substantially outperforms existing methods, pointing toward a future where we can extend scientific monitoring far beyond where our sensors physically reach.