arXiv subjects

Tongyao Pang

Publications and source records attributed to Tongyao Pang.

4 recordsLinked to original sources

arXiv2026

Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models

Diffusion models learn to reverse a predefined corruption process, but sampling still requires a costly time discretization and depends on the chosen noise schedule. We study these two issues for variance-preserving diffusions with matrix-valued schedules. Our analysis transfers reverse-time discretization errors to the forward corruption law and treats two numerical schemes within a common framework. The first freezes the score and yields, through a matrix-sensitive local comparison and forward information dissipation, an ambient-dimensional step complexity with leading factor $d/\varepsilon^2$ for KL accuracy $\varepsilon^2$. The second keeps the known Gaussian drift exact and freezes the posterior mean. For data of metric-entropy dimension $k$, a forward Markov identity, an anisotropic covering estimate, and Stieltjes integration by parts give the corresponding factor $k\log k/\varepsilon^2$. In both cases, the proof identifies a local error, accumulates it through the forward evolution, and inserts the result into a common KL decomposition. The local errors further provide directional criteria for matrix schedules and an asymptotically optimal square-root adaptive grid. A high-dimensional Gaussian-mixture experiment illustrates the resulting schedule and grid improvements.

math.ST↗

arXiv2026

A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors

Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior.

stat.ML↗

arXiv2026

Outlier-Robust Diffusion Solvers for Inverse Problems

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases. The code is available at https://github.com/StarNextDay/Robust-DAPS.git.

cs.CV↗

arXiv2026

Enhancing Low-resolution Image Representation Through Normalizing Flows

Low-resolution image representation is a special form of sparse representation that retains only low-frequency information while discarding high-frequency components. This property reduces storage and transmission costs and benefits various image processing tasks. However, a key challenge is to preserve essential visual content while maintaining the ability to accurately reconstruct the original images. This work proposes LR2Flow, a nonlinear framework that learns low-resolution image representations by integrating wavelet tight frame blocks with normalizing flows. We conduct a reconstruction error analysis of the proposed network, which demonstrates the necessity of designing invertible neural networks in the wavelet tight frame domain. Experimental results on various tasks, including image rescaling, compression, and denoising, demonstrate the effectiveness of the learned representations and the robustness of the proposed framework.

cs.CV↗