The paper, posted on arXiv, considers a generative modeling problem where each individual sample must satisfy a prescribed constraint with a user-specified probability. This differs from population-level constraints that only hold on average, making the requirement stricter and more practical for applications such as safety-critical generation.
The authors propose a primal-dual flow matching approach to address this setting. According to the abstract, the method begins with a population-level constrained negative objective, suggesting a link between population-level formulations and the sample-wise constraint. The full derivation is not available in the abstract text.
The paper is listed under arXiv identifier 2610.12699. The available abstract describes the problem and the proposed method but does not include experimental results or comparisons, so the practical performance of the approach is not detailed in the source.