Selected work

Representative Papers

Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps

Oct 07, 2026

This work addresses the challenge of posterior sampling with diffusion priors under nonlinear, non-differentiable forward models by proposing a method termed Diffusion Waltz. The approach constructs Markov chain Monte Carlo (MCMC) proposal distributions through SDEdit-style noising and denoising, and incorporates observational information via a gradient-free ensemble Kalman update. A Metropolis-Hastings correction is subsequently applied to achieve exact posterior sampling without requiring prior density evaluation. Evaluated on Navier-Stokes initial condition recovery tasks, the proposed method significantly outperforms existing baselines across varying noise levels and degrees of nonlinearity, demonstrating both theoretical rigor and practical effectiveness.

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Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators

Aug 01, 2025

Fourier Neural Operators (FNOs) suffer from poor scalability due to over-parameterization and lack intrinsic uncertainty quantification (UQ), while existing posterior UQ methods compromise their geometric inductive bias. To address these issues, we propose DINOZAUR: the first FNO variant that embeds a heat-kernel diffusion process into the spectral multiplier design, replacing high-dimensional tensor parameters with a single time-varying scalar—enabling lightweight modeling. Concurrently, we introduce a Bayesian prior directly in the frequency domain, enabling geometrically consistent, calibration-aware UQ. DINOZAUR thus achieves both efficiency and reliability: it attains state-of-the-art or competitive accuracy across multiple PDE benchmarks, with significantly reduced parameter count and memory footprint, while producing spatially correlated, statistically calibrated uncertainty estimates.

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Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models

Jun 16, 2025

Diffusion models suffer from low conditional sampling accuracy, large time-dependent errors, and poor sampling efficiency in inverse problems such as image restoration. To address these issues, this paper proposes a training-free Bayesian posterior guidance framework. We first derive an analytical closed-form solution for the posterior score function under pure denoising—replacing conventional approximations—and then design a time-varying adaptive step-size strategy that explicitly minimizes single-step error, with empirical validation of its cross-task generalizability. Our method achieves state-of-the-art performance on denoising, colorization, stochastic inpainting, and super-resolution, while significantly reducing the number of sampling steps compared to DPS—thereby jointly improving both accuracy and efficiency.

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Recent publications

Latest Papers

Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps

Oct 07, 2026

This work addresses the challenge of posterior sampling with diffusion priors under nonlinear, non-differentiable forward models by proposing a method termed Diffusion Waltz. The approach constructs Markov chain Monte Carlo (MCMC) proposal distributions through SDEdit-style noising and denoising, and incorporates observational information via a gradient-free ensemble Kalman update. A Metropolis-Hastings correction is subsequently applied to achieve exact posterior sampling without requiring prior density evaluation. Evaluated on Navier-Stokes initial condition recovery tasks, the proposed method significantly outperforms existing baselines across varying noise levels and degrees of nonlinearity, demonstrating both theoretical rigor and practical effectiveness.

0 citationsRead paper

Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators

Aug 01, 2025

Fourier Neural Operators (FNOs) suffer from poor scalability due to over-parameterization and lack intrinsic uncertainty quantification (UQ), while existing posterior UQ methods compromise their geometric inductive bias. To address these issues, we propose DINOZAUR: the first FNO variant that embeds a heat-kernel diffusion process into the spectral multiplier design, replacing high-dimensional tensor parameters with a single time-varying scalar—enabling lightweight modeling. Concurrently, we introduce a Bayesian prior directly in the frequency domain, enabling geometrically consistent, calibration-aware UQ. DINOZAUR thus achieves both efficiency and reliability: it attains state-of-the-art or competitive accuracy across multiple PDE benchmarks, with significantly reduced parameter count and memory footprint, while producing spatially correlated, statistically calibrated uncertainty estimates.

0 citationsRead paper

Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models

Jun 16, 2025

Diffusion models suffer from low conditional sampling accuracy, large time-dependent errors, and poor sampling efficiency in inverse problems such as image restoration. To address these issues, this paper proposes a training-free Bayesian posterior guidance framework. We first derive an analytical closed-form solution for the posterior score function under pure denoising—replacing conventional approximations—and then design a time-varying adaptive step-size strategy that explicitly minimizes single-step error, with empirical validation of its cross-task generalizability. Our method achieves state-of-the-art performance on denoising, colorization, stochastic inpainting, and super-resolution, while significantly reducing the number of sampling steps compared to DPS—thereby jointly improving both accuracy and efficiency.

0 citationsRead paper