Schrödinger Bridge as Robustified Optimal Transport Flows

In many generative tasks where sample quality is paramount, diffusion models have become the method of choice over normalizing flows, despite the latter’s advantage in sampling efficiency. This work investigates the origins of this performance gap by focusing on flow-based models grounded in optimal transport (OT), particularly those trained under the flow matching paradigm. Our main result shows that diffusion models can be viewed as $\textbf{robustified}$ versions of OT-based flows: they implicitly solve a distributionally robust variant of the Kantorovich dual problem. This perspective intuitively explains their improved generalization and stability under noisy or imperfect training. Moreover, our analysis reveals a novel link of generative models to the persistency problem in discrete choice theory, offering new insight into the structural advantages of diffusion models and suggesting broader implications for robust generative modeling.