We formulate generative modeling as a path integral in which flow-based, diffusion-based, variational, and adversarial models arise as different evaluation principles for a single master action. Its Martin-Siggia-Rose-Janssen-de~Dominicis (MSRJD) form separates free from interacting probability flows and opens them to diagrammatic perturbation theory. The expansion yields a one-loop correction to deterministic samplers at no stochastic-sampling cost, which we validate on solvable and nonlinear drifts, where it reduces a 53 % tree-level error to 1.6 %. Imperfect learned scores enter as insertions and yield a response-weighted score-matching objective, and symmetry-equivariant drift design becomes an operator expansion with EFT power counting.
We introduce a novel generative modeling framework based on a discretized parabolic Monge–Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. Our method performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. We establish...
Nabarun Deb, Tengyuan Liang· Annals of Statistics· 0 citations
Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as...
David Li, Chanhyuk Lee, Jaehoon Yoo et al.· 0 citations
We introduce a new framework for one-step generative modelling on finite state spaces. To extend drifting beyond continuous domains, we use discrete Wasserstein geometry to define a target-relative KL gradient flow over the transitions of a reversible Markov kernel. We realize this probability flow at the particle leve...
Alessandro Micheli, Andrea Zerio, Samir Bhatt· 0 citations
Diffusion sampling can be viewed as imaginary-time annealing of probability densities. From a forward/backward Euclidean Schr\"odinger pair, we show that fixing the noising drift forces the reverse score term, and that the same logarithmic force is the one-sided imaginary-time counterdiabatic connection of a supersymme...
JIVE is introduced, a training-free framework that enhances generative diversity by injecting velocity perturbations aligned with the leading right singular subspace of the generator's endpoint Jacobian, which provably maximizes endpoint diversity while preserving sample quality.
Guang-Xun Zhang, Brian Cai, Boxuan Zhang et al.· 0 citations
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