Proposes a universal denoiser that outperforms the Bayes-optimal Tweedie's formula when the noise distribution is unknown.
March 30, 2026
Original Paper
Distributional Shrinkage I: Universal Denoiser Beyond Tweedie's Formula
arXiv · 2511.09500
The Takeaway
Using optimal transport and the Monge–Ampère equation, it achieves higher-order accuracy in signal recovery without needing to know the noise prior. This is a fundamental advance for any generative modeling or signal processing task where noise is non-Gaussian or poorly characterized.
From the abstract
We study the problem of denoising when only the noise level is known, not the noise distribution. Independent noise $Z$ corrupts a signal $X$, yielding the observation $Y = X + \sigma Z$ with known $\sigma \in (0,1)$. We propose \emph{universal} denoisers, agnostic to both signal and noise distributions, that recover the signal distribution $P_X$ from $P_Y$. When the focus is on distributional recovery of $P_X$ rather than on individual realizations of $X$, our denoisers achieve order-of-magnitu