W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
Diffusion schrödinger bridge with applications to score-based generative modeling.arXiv preprint arXiv:2106.01357
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Attention, diffusion maps, and magnetic Laplacians are different regimes of a single Markov geometry from pre-softmax query-scores, linked by a QK bidivergence and Schrödinger bridges into equilibrium, nonequilibrium, and driven dynamics.
Semi-dual optimal transport has a degenerate saddle-point structure equivalent to constrained optimization, with necessary and sufficient conditions derived for Monge map convergence independent of dual potential optimality.
The Ensemble Schrödinger Bridge filter adds a diffusion-based analysis step to ensemble prediction, enabling effective nonlinear data assimilation without structural model error or training.
A synthesis of diffusion-based simulation-based inference methods that address model misspecification, irregular observations, and missing data in scientific applications.
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One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
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The Diffusion-Attention Connection
Attention, diffusion maps, and magnetic Laplacians are different regimes of a single Markov geometry from pre-softmax query-scores, linked by a QK bidivergence and Schrödinger bridges into equilibrium, nonequilibrium, and driven dynamics.
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Stability of the Monge Map in Semi-Dual Optimal Transport
Semi-dual optimal transport has a degenerate saddle-point structure equivalent to constrained optimization, with necessary and sufficient conditions derived for Monge map convergence independent of dual potential optimality.
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The Ensemble Schr{\"o}dinger Bridge filter for Nonlinear Data Assimilation
The Ensemble Schrödinger Bridge filter adds a diffusion-based analysis step to ensemble prediction, enabling effective nonlinear data assimilation without structural model error or training.
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A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios
A synthesis of diffusion-based simulation-based inference methods that address model misspecification, irregular observations, and missing data in scientific applications.