Louis Thomas Hardin, better known as Moondog, was a blind avant-garde American musician who worked in a variety of genres including jazz and classical, invented a series of his own instruments, influenced a bunch of other composers including the American minimalists, made a lot of his living by begging and briefly appeared in a cloak and horned helmet (he loved Norse mythology) on Sixth Avenue in New York.
But never mind that.
Diffusion models and flow-based methods have achieved strong results in image generation, but often rely on costly iterative sampling. We introduce W-Flow, a framework that compresses a Wasserstein gradient flow into a one-step neural generator. By minimizing the Sinkhorn divergence, W-Flow transports a reference distribution toward the data distribution through efficient optimal-transport updates that capture global distributional discrepancies. We prove that, under suitable assumptions, the finite-sample training dynamics converge to the continuous-time distributional dynamics. Empirically, W-Flow sets a new state of the art in one-step ImageNet generation, with improved mode coverage and domain transfer. We will also discuss extensions using alternative energy functionals and applications to post-training.
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space R^3 . When the small rigid body shrinks to a point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier–Stokes equations in the full space. Based on some L^p − L^q estimates of the fluid–structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit. This is a joint work with Pei Su (Nantes).
