{"ID":2844662,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06042","arxiv_id":"2511.06042","title":"Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching","abstract":"We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (HJ) residual in the OT formulation with the original flow matching loss function. Our approach avoids inner optimization subproblems that are present in previous one-step OFM approaches. During the prediction stage, our approach supports both one-step (Brenier-map) and multi-step ODE sampling from the same learned potential, leveraging the straightness of the OT flow. We validate scalability and performance on standard OT benchmarks.","short_abstract":"We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (HJ) residual in the...","url_abs":"https://arxiv.org/abs/2511.06042","url_pdf":"https://arxiv.org/pdf/2511.06042v1","authors":"[\"Fanghui Song\",\"Zhongjian Wang\",\"Jiebao Sun\"]","published":"2025-11-08T15:30:55Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}