Pawsterior: Variational Flow Matching for Structured Simulation-Based Inference

Jorge Carrasco-Pollo, Floor Eijkelboom, Jan-Willem van de Meent
Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling, PMLR 326:75-87, 2026.

Abstract

We introduce Pawsterior, a variational flow-matching framework for improved and extended simulation-based inference (SBI). Many SBI problems involve posteriors constrained by structured domains—such as bounded physical parameters or hybrid discrete–continuous variables—yet standard flow-matching methods typically operate in unconstrained spaces. This mismatch leads to inefficient learning and difficulty respecting physical constraints. Our contributions are twofold. First, generalizing the geometric inductive bias of CatFlow, we formalize endpoint-induced affine geometric confinement, a principle that incorporates domain geometry directly into the inference process via a two-sided variational model. This formulation improves numerical stability during sampling and leads to consistently better posterior fidelity, as demonstrated by improved classifier two-sample test performance across standard SBI benchmarks. Second, and more importantly, our variational parameterization enables SBI tasks involving discrete latent structure (e.g., switching systems) that are fundamentally incompatible with conventional flow-matching approaches. By addressing both geometric constraints and discrete latent structure, Pawsterior provides a principled way to apply flow-matching in a broader range of structured SBI settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v326-carrasco-pollo26a, title = {{P}awsterior: {V}ariational {F}low {M}atching for {S}tructured {S}imulation-{B}ased {I}nference}, author = {Carrasco-Pollo, Jorge and Eijkelboom, Floor and van de Meent, Jan-Willem}, booktitle = {Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling}, pages = {75--87}, year = {2026}, editor = {Pouplin, Alison and Vadgama, Sharvaree and Bekkers, Erik and Kaba, Sékou-Oumar and Lawrence, Hannah and Lecha, Manuel and Baker, Elizabeth and Suk, Julian and Walters, Robin and Tomczak, Jakub and Jegelka, Stefanie}, volume = {326}, series = {Proceedings of Machine Learning Research}, month = {26 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v326/main/assets/carrasco-pollo26a/carrasco-pollo26a.pdf}, url = {https://proceedings.mlr.press/v326/carrasco-pollo26a.html}, abstract = {We introduce Pawsterior, a variational flow-matching framework for improved and extended simulation-based inference (SBI). Many SBI problems involve posteriors constrained by structured domains—such as bounded physical parameters or hybrid discrete–continuous variables—yet standard flow-matching methods typically operate in unconstrained spaces. This mismatch leads to inefficient learning and difficulty respecting physical constraints. Our contributions are twofold. First, generalizing the geometric inductive bias of CatFlow, we formalize endpoint-induced affine geometric confinement, a principle that incorporates domain geometry directly into the inference process via a two-sided variational model. This formulation improves numerical stability during sampling and leads to consistently better posterior fidelity, as demonstrated by improved classifier two-sample test performance across standard SBI benchmarks. Second, and more importantly, our variational parameterization enables SBI tasks involving discrete latent structure (e.g., switching systems) that are fundamentally incompatible with conventional flow-matching approaches. By addressing both geometric constraints and discrete latent structure, Pawsterior provides a principled way to apply flow-matching in a broader range of structured SBI settings.} }
Endnote
%0 Conference Paper %T Pawsterior: Variational Flow Matching for Structured Simulation-Based Inference %A Jorge Carrasco-Pollo %A Floor Eijkelboom %A Jan-Willem van de Meent %B Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling %C Proceedings of Machine Learning Research %D 2026 %E Alison Pouplin %E Sharvaree Vadgama %E Erik Bekkers %E Sékou-Oumar Kaba %E Hannah Lawrence %E Manuel Lecha %E Elizabeth Baker %E Julian Suk %E Robin Walters %E Jakub Tomczak %E Stefanie Jegelka %F pmlr-v326-carrasco-pollo26a %I PMLR %P 75--87 %U https://proceedings.mlr.press/v326/carrasco-pollo26a.html %V 326 %X We introduce Pawsterior, a variational flow-matching framework for improved and extended simulation-based inference (SBI). Many SBI problems involve posteriors constrained by structured domains—such as bounded physical parameters or hybrid discrete–continuous variables—yet standard flow-matching methods typically operate in unconstrained spaces. This mismatch leads to inefficient learning and difficulty respecting physical constraints. Our contributions are twofold. First, generalizing the geometric inductive bias of CatFlow, we formalize endpoint-induced affine geometric confinement, a principle that incorporates domain geometry directly into the inference process via a two-sided variational model. This formulation improves numerical stability during sampling and leads to consistently better posterior fidelity, as demonstrated by improved classifier two-sample test performance across standard SBI benchmarks. Second, and more importantly, our variational parameterization enables SBI tasks involving discrete latent structure (e.g., switching systems) that are fundamentally incompatible with conventional flow-matching approaches. By addressing both geometric constraints and discrete latent structure, Pawsterior provides a principled way to apply flow-matching in a broader range of structured SBI settings.
APA
Carrasco-Pollo, J., Eijkelboom, F. & van de Meent, J.. (2026). Pawsterior: Variational Flow Matching for Structured Simulation-Based Inference. Proceedings of GRaM: the Second Edition of the Workshop on Geometry-grounded Representation Learning and Generative Modeling, in Proceedings of Machine Learning Research 326:75-87 Available from https://proceedings.mlr.press/v326/carrasco-pollo26a.html.

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