# TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing

arXiv: https://arxiv.org/abs/2608.26219 · HTML: https://mlsanity.com/paper/2608.26219/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks](https://mlsanity.com/paper/2401.11611/) (2024)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data](https://mlsanity.com/paper/2311.04829/) (2023)
- [Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations](https://mlsanity.com/paper/2505.09284/) (2025)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Deep Bayesian Filter for Bayes-faithful Data Assimilation](https://mlsanity.com/paper/2405.18674/) (2024)
- [Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation](https://mlsanity.com/paper/2410.13794/) (2024)
- [ForcingDAS: Unified and Robust Data Assimilation via Diffusion Forcing](https://mlsanity.com/paper/2605.14285/) (2026)

## Abstract (arXiv)

Reconstructing continuous physical fields from sparse measurements is central to scientific monitoring, inverse modeling, and digital-twin construction. Generative reconstruction has recently emerged as a promising paradigm for this task by learning data-driven physical priors that complete plausible full fields from limited observations. However, existing methods largely assume fixed, batch conditioning, whereas real sensing systems often produce structured streams: probes scan local regions, instruments observe moving fields of view, and communication constraints may leave entire frames missing. We propose TRACE, a retrospective streaming generative reconstruction framework for physical fields under structured sensing. TRACE performs approximate Bayesian inference in a learned continuous-coordinate latent space, converting sparse off-grid measurements into generative latent evidence, fusing it with a state-space temporal prior through Kalman-style filtering, and refining under-observed past frames via retrospective smoothing. Experiments on active matter, ocean sound-speed fields, and supernova simulations show that TRACE matches or surpasses frame-wise generative reconstructors, offline spatiotemporal methods, and streaming data-assimilation baselines in reconstruction quality under temporally sparse and spatially localized sensing protocols.