Learning Unbiased Permutations via Flow Matching

• URL: http://arxiv.org/abs/2605.16755v1
• Date: Sat, 16 May 2026 02:10:35 GMT
• Title: Learning Unbiased Permutations via Flow Matching
• Abstract summary: PermFlow is a conditional flow matching framework for learning permutations.<n>It captures multimodal permutation distributions rather than collapsing them to a single mode.<n>It achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity.
• Score: 22.51828421737954
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.

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