Laplace-Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation
Sampling from an unnormalized target density by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal law. Two exact identities are available: Tweedie's identity and a target-score identity, each yielding unbiased finite-reference score estimators for the OU-marginal score. Score estimators induced by scalar blends of Tweedie and TSI score estimators can reduce variance, but they are too rigid for singular or strongly anisotropic targets. We formulate blended score estimation as a conditional risk-minimization problem over matrix valued blending coefficients, referred to as gates. Our central result is to show the optimal matrix valued gate for blen...
| Authors | Alois Duston, Tan Bui-Thanh |
|---|---|
| Primary category | math.ST |
| Published | 23 June 2026 |
| Last updated at source | 1 July 2026 |
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