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Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation

arXiv 2601.07013 ↗First posted 11 Jan 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters -- show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 59 references that are in the map. First posted on arXiv 11 Jan 2026.

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References · 24

  1. 2022Generative Adversarial Networkscited by 5,627
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12 more
  1. 2019Coupling techniques for nonlinear ensemble filteringcited by 48
  2. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 25
  3. 2022Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularizationcited by 17
  4. 2018Structural Consistency and Controllability for Diverse Colorizationcited by 15
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  12. 2023XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting with High Volatilitycited by 3

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  5. 2025Normalizing Flows are Capable Models for Continuous Control
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