Research map / Probabilistic and scientific modeling / Variational and generative sampling
Compatible Likelihoods for Flow Matching on Manifolds
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Shows that a recently proposed likelihood-based extension of Riemannian flow matching can be globally optimized by a velocity field that pushes samples away from the data, and identifies "compatibility" as the property that prevents this failure.
Problem
Flow matching on non-Euclidean manifolds with likelihood-based objectives: whether the population minimizer of such an objective recovers the correct marginal velocity field.
Approach
Defines compatibility of a likelihood-based flow matching objective (its population minimizer recovers the marginal velocity field) and exhibits a 1D flat torus counterexample where a recent extension is globally optimized by an anti-data velocity field.
Key results
- On the 1D flat torus, a distribution exists for which a recently proposed extension of Riemannian flow matching is globally optimized by a velocity field that pushes samples away from the data distribution.
Surprising findings
- A recently proposed likelihood-based extension of Riemannian flow matching is globally optimized by a velocity field that pushes samples away from the data distribution.
Limitations
- Full text unavailable; analysis limited to abstract-level claims.
Experimental setup
Builds on: Riemannian flow matching
Closest papers by meaning
- Flow Matching on General Geometries (ICLR 2024 · similarity 0.91)
- Metric Flow Matching for Smooth Interpolations on the Data Manifold (NeurIPS 2024 · similarity 0.90)
- Categorical Flow Matching on Statistical Manifolds (NeurIPS 2024 · similarity 0.90)
- Learning Distributions on Manifolds with Free-Form Flows (NeurIPS 2024 · similarity 0.87)
- Injective flows for star-like manifolds (ICLR 2025 · similarity 0.87)
- Flow Matching from Viewpoint of Proximal Operators (NeurIPS 2026 · similarity 0.87)
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