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Hong Gu

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Computer Vision math.AP Methodology

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preprint2026arXiv

HDRFace: Rethinking Face Restoration with High-Dimensional Representation

Face restoration under complex degradations still remains an ill-posed inverse problem due to severe information loss. Although diffusion models benefit from strong generative priors, most methods still condition only on low-quality inputs, making it difficult to recover identity-critical details under heavy degradations. In this work, we propose HDRFace, a High-Dimensional Representation conditioned Face restoration framework that injects semantically rich priors into the conditional flow without modifying the generative backbone. Our pipeline first obtains a structurally reliable intermediate restoration with an off-the-shelf restorer, then uses a pretrained high-dimensional feature encoder to extract fine-grained facial representations from both the low-quality input and the intermediate result, and injects them as additional conditions for generation. We further introduce SDFM, a Structure-Detail aware adaptive Fusion Mechanism that emphasizes global constraints during structure modeling and strengthens representation guidance during detail synthesis, balancing structural consistency and detail fidelity. To validate the generalization ability of our method, we implement the proposed framework on two generative models, SD V2.1-base and Qwen-Image, and consistently observe stable and coherent performance gains across different architectures.

preprint2026arXiv

Tuning-Free Adaptive Style Incorporation for Structure-Consistent Text-Driven Style Transfer

In this work, we target the task of text-driven style transfer in the context of text-to-image (T2I) diffusion models. The main challenge is consistent structure preservation while enabling effective style transfer effects. The past approaches in this field directly concatenate the content and style prompts for a prompt-level style injection, leading to unavoidable structure distortions. In this work, we propose a novel solution to the text-driven style transfer task, namely, Adaptive Style Incorporation~(ASI), to achieve fine-grained feature-level style incorporation. It consists of the Siamese Cross-Attention~(SiCA) to decouple the single-track cross-attention to a dual-track structure to obtain separate content and style features, and the Adaptive Content-Style Blending (AdaBlending) module to couple the content and style information from a structure-consistent manner. Experimentally, our method exhibits much better performance in both structure preservation and stylized effects.

preprint2016arXiv

Prior Distributions for Ranking Problems

The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank potential projects by profitability; or science, where we may want to rank variables potentially associated with some trait by the strength of the association. Most approaches to this problem are empirical Bayesian, where we use the data to estimate the hyperparameters of the prior distribution, then use that distribution to estimate the unobserved parameter values. There are a number of different approaches to this problem, based on different loss functions for mis-ranking units. However, little has been done on the choice of prior distribution. Typical approaches involve choosing a conjugate prior for convenience, and estimating the hyperparameters by MLE from the whole dataset. In this paper, we look in more detail at the effect of choice of prior distribution on Bayesian ranking. We focus on the use of posterior mean for ranking, but many of our conclusions should apply to other ranking criteria, and it is not too difficult to adapt our methods to other choices of prior distributions.

preprint2016arXiv

The Adequate Bootstrap

There is a fundamental disconnect between what is tested in a model adequacy test, and what we would like to test. The usual approach is to test the null hypothesis "Model M is the true model." However, Model M is never the true model. A model might still be useful even if we have enough data to reject it. In this paper, we present a technique to assess the adequacy of a model from the philosophical standpoint that we know the model is not true, but we want to know if it is useful. Our solution to this problem is to measure the parameter uncertainty in our estimates caused by the model uncertainty. We use bootstrap inference on samples of a smaller size, for which the model cannot be rejected. We use a model adequacy test to choose a bootstrap size with limited probability of rejecting the model and perform inference for samples of this size based on a nonparametric bootstrap. Our idea is that if we base our inference on a sample size at which we do not reject the model, then we should be happy with this inference, because we would have been confident in it if our original dataset had been this size.

preprint2015arXiv

Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries

We consider Fisher-KPP equation with advection: $u_t=u_{xx}-βu_x+f(u)$ for $x\in (g(t),h(t))$, where $g(t)$ and $h(t)$ are two free boundaries satisfying Stefan conditions. This equation is used to describe the population dynamics in advective environments. We study the influence of the advection coefficient $-β$ on the long time behavior of the solutions. We find two parameters $c_0$ and $β^*$ with $β^*>c_0>0$ which play key roles in the dynamics, here $c_0$ is the minimal speed of the traveling waves of Fisher-KPP equation. More precisely, by studying a family of the initial data $\{ σϕ\}_{σ>0}$ (where $ϕ$ is some compactly supported positive function), we show that, (1) in case $β\in (0,c_0)$, there exists $σ^*\geqslant0$ such that spreading happens when $σ> σ^*$ and vanishing happens when $σ\in (0,σ^*]$; (2) in case $β\in (c_0,β^*)$, there exists $σ^*>0$ such that virtual spreading happens when $σ>σ^*$ (i.e., $u(t,\cdot;σϕ)\to 0$ locally uniformly in $[g(t),\infty)$ and $u(t,\cdot + ct;σϕ)\to 1$ locally uniformly in $\R$ for some $c>β-c_0$), vanishing happens when $σ\in (0,σ^*)$, and in the transition case $σ=σ^*$, $u(t, \cdot+o(t);σϕ)\to V^*(\cdot-(β-c_0)t )$ uniformly, the latter is a traveling wave with a "big head" near the free boundary $x=(β-c_0)t$ and with an infinite long "tail" on the left; (3) in case $β= c_0$, there exists $σ^*>0$ such that virtual spreading happens when $σ> σ^*$ and $u(t,\cdot;σϕ)\to 0$ uniformly in $[g(t),h(t)]$ when $σ\in (0,σ^*]$; (4) in case $β\geqslant β^*$, vanishing happens for any solution.

preprint2013arXiv

Different Asymptotic Spreading Speeds Induced by Advection in a Diffusion Problem with Free Boundaries

In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that is, the solution converges to a positive constant), we use phase plane analysis and upper/lower solutions to prove that the rightward and leftward asymptotic spreading speeds exist, both are positive constants. Moreover, one of them is bigger and the other is smaller than the spreading speed in the corresponding problem without advection term.