Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
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Anisotropic SPDEs preserve geometric data structure over longer timescales in score-based generative modeling, yielding better image quality than standard SDE baselines and flow matching in unconditional and conditional tasks.
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Higher order approximation of nonlinear SPDEs with additive space-time white noise
Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
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Score-Based Generative Modeling through Anisotropic Stochastic Partial Differential Equations
Anisotropic SPDEs preserve geometric data structure over longer timescales in score-based generative modeling, yielding better image quality than standard SDE baselines and flow matching in unconditional and conditional tasks.