Co-Evolving Interpolants and Flows via Path-Flow Alignment

We study path–flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving path network and a flow network using the same alignment loss: the flow learns to match the path velocity, and the path learns to align its velocity to the current flow. Although every fixed learned path defines a valid flow-matching objective, the alignment loss alone is not a reliable criterion for path learning. We identify *path overfitting*, a failure mode in which the alignment loss decreases while sample quality worsens. We trace this failure to low-entropy bottlenecks in the induced probability path, where the learned interpolant routes samples through overly concentrated intermediate marginals. Motivated by this diagnosis, we introduce a stochastic path regularizer that hides part of the source information from the path network while preserving exact endpoints. The resulting regularized objective controls entropy collapse and makes joint path–flow training effective. On ImageNet-$256\times 256$ with SiT backbones, our method consistently improves FID across model scales, extends to model-guidance training, and leaves the inference-time architecture and sampler unchanged. Code is available at https://anonymous.4open.science/r/traj_opt_paper-4D80.