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arXiv · 2610.38273

NAGO: Noise-Aware Generative Operator via Flow Matching

Guanyu Chen·Shengze Xu·Pengwei Liu·Xingyu Ren·Pengkai Wang·Antonios Armaou·Tieyong Zeng·Dong Ni
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Abstract

We introduce NAGO, a noise-aware generative operator for efficient sampling from invariant measures of stochastic partial differential equations (SPDEs) in function space. Our central idea is to treat the source measure as a design variable rather than a fixed Gaussian default. We establish admissibility conditions for well-defined infinite-dimensional flows and show that the finite-band source--target covariance ratio controls the spectral stiffness of the marginal velocity field. This analysis yields an admissibility-constrained spectral-matching rule: choose a source that is sufficiently rough for well-posedness, then minimize covariance mismatch over the resolved Fourier modes. On three representative stochastic-field benchmarks, this source design improves few-step spectral accuracy and several complementary distributional and physical statistics. In a controlled Matern-field ablation, it reduces the accurate RK4 budget from about 30 steps for Gaussian functional flow matching to 3--5 steps, a $6$--$10\times$ reduction in neural ODE evaluations. These gains are strongest for stationary multiscale fields and depend on the metric, resolution, and guidance protocol.

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Guanyu Chen, Shengze Xu, Pengwei Liu, Xingyu Ren, Pengkai Wang, Antonios Armaou, Tieyong Zeng, Dong Ni. 2026-10-31. NAGO: Noise-Aware Generative Operator via Flow Matching. https://arxiv.org/abs/2610.38273

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