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Error Bounds for Flow Matching Methods
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abstract
Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the $L^2$ loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an $L^2$ bound on the approximation error and a certain regularity condition on the data distributions.
Forward citations
Cited by 4 Pith papers
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Fast Score-Based Sampling via Log-Concave Reductions
Score-based sampling reduces to a short sequence of strongly log-concave sampling problems, giving √d polylog(1/ε) complexity bounds and logarithmic dependence on the condition number for log-concave targets.
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Generalization bounds for score-based generative models: a synthetic proof
Score-based generative models achieve minimax optimal W1 rates n^{-(β+1)/(2β+d)} over β-Hölder densities, up to polylog factors.
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Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
A TV convergence bound O(d^{7/4} ε^{1/2} + d(dH)^p) is proved for p-th order (exponential) Runge-Kutta samplers of probability-flow ODEs under C² smoothness of the learned score.
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Safe Vision Language Action Models via Barrier Enhanced Flow Matching
A control-barrier-function safety filter embedded in flow-matching denoising generates safe robot action chunks without retraining the base VLA model.
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