Shigui Li

Wei Chen, Jiacheng Li, Shigui Li et al.

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation. Our code can be found in https://github.com/Hoemr/OpenDRE.git.

Shigui Li, Wei Chen, Delu Zeng

Diffusion models (DMs) have made significant progress in the fields of image, audio, and video generation. One downside of DMs is their slow iterative process. Recent algorithms for fast sampling are designed from the perspective of differential equations. However, in higher-order algorithms based on Taylor expansion, estimating the derivative of the score function becomes intractable due to the complexity of large-scale, well-trained neural networks. Driven by this motivation, in this work, we introduce the recursive difference (RD) method to calculate the derivative of the score function in the realm of DMs. Based on the RD method and the truncated Taylor expansion of score-integrand, we propose SciRE-Solver with the convergence order guarantee for accelerating sampling of DMs. To further investigate the effectiveness of the RD method, we also propose a variant named SciREI-Solver based on the RD method and exponential integrator. Our proposed sampling algorithms with RD method attain state-of-the-art (SOTA) FIDs in comparison to existing training-free sampling algorithms, across both discrete-time and continuous-time pre-trained DMs, under various number of score function evaluations (NFE). Remarkably, SciRE-Solver using a small NFEs demonstrates promising potential to surpass the FID achieved by some pre-trained models in their original papers using no fewer than $1000$ NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DM and of $3.15$ FID with $84$ NFE for discrete-time DM on CIFAR-10, as well as of $2.17$ (2.02) FID with $18$ (50) NFE for discrete-time DM on CelebA 64$\times$64.

Wei Chen, Shian Du, Shigui Li et al.

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale architectures address this by progressively reducing latent dimensions while preserving reversibility. Existing multi-scale architectures use simple, static channel-wise splitting, limiting expressiveness. To improve this, we introduce a regularized, feature-dependent $\mathtt{Shuffle}$ operation and integrate it into vanilla multi-scale architecture. This operation adaptively generates channel-wise weights and shuffles latent variables before splitting them. We observe that such operation guides the variables to evolve in the direction of entropy increase, hence we refer to NFs with the $\mathtt{Shuffle}$ operation as \emph{Entropy-Informed Weighting Channel Normalizing Flow} (EIW-Flow). Extensive experiments on CIFAR-10, CelebA, ImageNet, and LSUN demonstrate that EIW-Flow achieves state-of-the-art density estimation and competitive sample quality for deep generative modeling, with minimal computational overhead.

Jian Xu, Zhiqi Lin, Shigui Li et al.

Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in Bayesian Last Layer (BLL) models limits their expressive capacity when faced with non-Gaussian, outlier-rich, or high-dimensional datasets. To address this shortfall, we introduce a novel approach that combines diffusion techniques and implicit priors for variational learning of Bayesian last layer weights. This method leverages implicit distributions for modeling weight priors in BLL, coupled with diffusion samplers for approximating true posterior predictions, thereby establishing a comprehensive Bayesian prior and posterior estimation strategy. By delivering an explicit and computationally efficient variational lower bound, our method aims to augment the expressive abilities of BLL models, enhancing model accuracy, calibration, and out-of-distribution detection proficiency. Through detailed exploration and experimental validation, We showcase the method's potential for improving predictive accuracy and uncertainty quantification while ensuring computational efficiency.

Shigui Li, Wei Chen, Delu Zeng

Diffusion models (DMs) excel in image generation, but suffer from slow inference and the training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate the denoising inference, they lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5\% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25\% (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts. Code is available at https://github.com/ShiguiLi/EVODiff.

Wei Chen, Shigui Li, Jiacheng Li et al.

Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for \textbf{robust}, \textbf{stable} and \textbf{efficient} density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schr{ö}dinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schr{ö}dinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.

Jian Xu, Wei Chen, Shigui Li et al.

Diffusion models have achieved remarkable success in low-light image enhancement through Retinex-based decomposition, yet their requirement for hundreds of iterative sampling steps severely limits practical deployment. While recent consistency models offer promising one-step generation for \textit{unconditional synthesis}, their application to \textit{conditional enhancement} remains unexplored. We present \textbf{Consist-Retinex}, the first framework adapting consistency modeling to Retinex-based low-light enhancement. Our key insight is that conditional enhancement requires fundamentally different training dynamics than unconditional generation standard consistency training focuses on low-noise regions near the data manifold, while conditional mapping critically depends on large-noise regimes that bridge degraded inputs to enhanced outputs. We introduce two core innovations: (1) a \textbf{dual-objective consistency loss} combining temporal consistency with ground-truth alignment under randomized time sampling, providing full-spectrum supervision for stable convergence; and (2) an \textbf{adaptive noise-emphasized sampling strategy} that prioritizes training on large-noise regions essential for one-step conditional generation. On VE-LOL-L, Consist-Retinex achieves \textbf{state-of-the-art performance with single-step sampling} (\textbf{PSNR: 25.51 vs. 23.41, FID: 44.73 vs. 49.59} compared to Diff-Retinex++), while requiring only \textbf{1/8 of the training budget} relative to the 1000-step Diff-Retinex baseline.

Wei Chen, Shigui Li, Jiacheng Li et al.

Estimating density ratios is a fundamental problem in machine learning, but existing methods often trade off accuracy for efficiency. We propose \textit{Interval-annealed Secant Alignment Density Ratio Estimation (ISA-DRE)}, a framework that enables accurate, any-step estimation without numerical integration. Instead of modeling infinitesimal tangents as in prior methods, ISA-DRE learns a global secant function, defined as the expectation of all tangents over an interval, with provably lower variance, making it more suitable for neural approximation. This is made possible by the \emph{Secant Alignment Identity}, a self-consistency condition that formally connects the secant with its underlying tangent representations. To mitigate instability during early training, we introduce \emph{Contraction Interval Annealing}, a curriculum strategy that gradually expands the alignment interval during training. This process induces a contraction mapping, which improves convergence and training stability. Empirically, ISA-DRE achieves competitive accuracy with significantly fewer function evaluations compared to prior methods, resulting in much faster inference and making it well suited for real-time and interactive applications.