mlsanityData to 14 Oct 2026

An invertible generative model for forward and inverse problems

arXiv 2509.03910 ↗First posted 4 Sep 2025stat.ML cs.LG math.PRcited by 2

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Abstract (arXiv)

We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.e., sampling from the likelihood) and inference (i.e., sampling from the posterior). We call such a generative model a Reversible Simulator. We first construct an explicit instance of a reversible simulator by combining lower and upper triangular normalizing flows associated with conditional sampling into a single invertible map. We then establish basic structural properties of this construction, investigate its non-uniqueness, and derive a variational formulation that enables the generative model to be trained directly from paired samples. Finally, we illustrate the proposed framework on analytically tractable and stylized numerical examples, demonstrating its potential as a unified approach to conditional generative modeling for forward and inverse problems.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 38 of its 54 references that are in the map. First posted on arXiv 4 Sep 2025.

Builds on

38 of 54 references.

References · 38

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26 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
  2. 2026Twist Flow for Inverse Problemscited by 0