Domain Transfer Becomes Identifiable via a Single Alignment

• URL: http://arxiv.org/abs/2605.17918v1
• Date: Mon, 18 May 2026 06:26:51 GMT
• Title: Domain Transfer Becomes Identifiable via a Single Alignment
• Abstract summary: Domain transfer maps source to target distributions.<n>Push-forward mappings are generally non-identifiable.<n>Measures-preserving automorphisms (MPAs) preserve marginals while altering cross-domain correspondences.
• Score: 16.77630551061651
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Domain transfer (DT) maps source to target distributions and supports tasks such as unsupervised image-to-image translation, single-cell analysis, and cross-platform medical imaging. However, DT is fundamentally ill-posed: push-forward mappings are generally non-identifiable, as measure-preserving automorphisms (MPAs) preserve marginals while altering cross-domain correspondences, leading to content-misaligned translation. Recent work shows that MPAs can be eliminated by jointly transferring multiple corresponding source/target conditional distributions, but supervision signals labeling such conditionals are not always available in practice. We develop an alternative route to DT identifiability. Under a structural sparsity condition on the Jacobian support pattern, we show that distribution matching together with a single paired anchor sample suffices to identify the ground-truth transfer -- requiring substantially less supervision than prior approaches. To enable practical high-dimensional learning, we further propose an efficient Jacobian sparsity regularizer based on randomized masked finite differences, yielding a scalable surrogate without explicit Jacobian evaluation. Empirical results on synthetic and real-world DT tasks validate the theory.

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