Puheng Li

Haotian Ye, Kaiwen Zheng, Jiashu Xu et al. · gatech

Aligning generative diffusion models with human preferences via reinforcement learning (RL) is critical yet challenging. Most existing algorithms are often vulnerable to reward hacking, such as quality degradation, over-stylization, or reduced diversity. Our analysis demonstrates that this can be attributed to the inherent limitations of their regularization, which provides unreliable penalties. We introduce Data-regularized Diffusion Reinforcement Learning (DDRL), a novel framework that uses the forward KL divergence to anchor the policy to an off-policy data distribution. Theoretically, DDRL enables robust, unbiased integration of RL with standard diffusion training. Empirically, this translates into a simple yet effective algorithm that combines reward maximization with diffusion loss minimization. With over a million GPU hours of experiments and ten thousand double-blind human evaluations, we demonstrate on high-resolution video generation tasks that DDRL significantly improves rewards while alleviating the reward hacking seen in baselines, achieving the highest human preference and establishing a robust and scalable paradigm for diffusion post-training.

Puheng Li, James Zou, Linjun Zhang

Algorithmic fairness plays an increasingly critical role in machine learning research. Several group fairness notions and algorithms have been proposed. However, the fairness guarantee of existing fair classification methods mainly depends on specific data distributional assumptions, often requiring large sample sizes, and fairness could be violated when there is a modest number of samples, which is often the case in practice. In this paper, we propose FaiREE, a fair classification algorithm that can satisfy group fairness constraints with finite-sample and distribution-free theoretical guarantees. FaiREE can be adapted to satisfy various group fairness notions (e.g., Equality of Opportunity, Equalized Odds, Demographic Parity, etc.) and achieve the optimal accuracy. These theoretical guarantees are further supported by experiments on both synthetic and real data. FaiREE is shown to have favorable performance over state-of-the-art algorithms.

Puheng Li, Zhong Li, Huishuai Zhang et al.

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world applications, a theoretical understanding of their generalization capabilities remains underdeveloped. This work embarks on a comprehensive theoretical exploration of the generalization attributes of diffusion models. We establish theoretical estimates of the generalization gap that evolves in tandem with the training dynamics of score-based diffusion models, suggesting a polynomially small generalization error ($O(n^{-2/5}+m^{-4/5})$) on both the sample size $n$ and the model capacity $m$, evading the curse of dimensionality (i.e., not exponentially large in the data dimension) when early-stopped. Furthermore, we extend our quantitative analysis to a data-dependent scenario, wherein target distributions are portrayed as a succession of densities with progressively increasing distances between modes. This precisely elucidates the adverse effect of "modes shift" in ground truths on the model generalization. Moreover, these estimates are not solely theoretical constructs but have also been confirmed through numerical simulations. Our findings contribute to the rigorous understanding of diffusion models' generalization properties and provide insights that may guide practical applications.

Puheng Li, Tijana Zrnic, Emmanuel Candès

Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to improve estimation accuracy by prioritizing the collection of labels where the model is most uncertain. The drawback, however, is that inaccurate uncertainty estimates can make active sampling produce highly noisy results, potentially worse than those from naive uniform sampling. In this work, we present robust sampling strategies for active statistical inference. Robust sampling ensures that the resulting estimator is never worse than the estimator using uniform sampling. Furthermore, with reliable uncertainty estimates, the estimator usually outperforms standard active inference. This is achieved by optimally interpolating between uniform and active sampling, depending on the quality of the uncertainty scores, and by using ideas from robust optimization. We demonstrate the utility of the method on a series of real datasets from computational social science and survey research.

Haotian Ye, Qiyuan He, Jiaqi Han et al.

Accurate and efficient discrete video tokenization is essential for long video sequences processing. Yet, the inherent complexity and variable information density of videos present a significant bottleneck for current tokenizers, which rigidly compress all content at a fixed rate, leading to redundancy or information loss. Drawing inspiration from Shannon's information theory, this paper introduces InfoTok, a principled framework for adaptive video tokenization. We rigorously prove that existing data-agnostic training methods are suboptimal in representation length, and present a novel evidence lower bound (ELBO)-based algorithm that approaches theoretical optimality. Leveraging this framework, we develop a transformer-based adaptive compressor that enables adaptive tokenization. Empirical results demonstrate state-of-the-art compression performance, saving 20% tokens without influence on performance, and achieving 2.3x compression rates while still outperforming prior heuristic adaptive approaches. By allocating tokens according to informational richness, InfoTok enables a more compressed yet accurate tokenization for video representation, offering valuable insights for future research.

Jiaqi Han, Juntong Shi, Puheng Li et al.

Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive compute, recent works resort to the feature caching and reusing scheme that skips network evaluations at selected diffusion steps by using cached features in previous steps. However, their preliminary design solely relies on local approximation, causing errors to grow rapidly with large skips and leading to degraded sample quality at high speedups. In this work, we propose spectral diffusion feature forecaster (Spectrum), a training-free approach that enables global, long-range feature reuse with tightly controlled error. In particular, we view the latent features of the denoiser as functions over time and approximate them with Chebyshev polynomials. Specifically, we fit the coefficient for each basis via ridge regression, which is then leveraged to forecast features at multiple future diffusion steps. We theoretically reveal that our approach admits more favorable long-horizon behavior and yields an error bound that does not compound with the step size. Extensive experiments on various state-of-the-art image and video diffusion models consistently verify the superiority of our approach. Notably, we achieve up to 4.79$\times$ speedup on FLUX.1 and 4.67$\times$ speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.

Jiaqi Han, Puheng Li, Qiushan Guo et al.

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator to compress this evolution into one-step generation. We instantiate the energy functional with the Sinkhorn divergence, which yields an efficient optimal-transport-based update rule that captures global distributional discrepancy and improves coverage of the target distribution. We further prove that the finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. Empirically, W-Flow sets a new state of the art for one-step ImageNet 256$\times$256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100$\times$ faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.

Zhanran Lin, Puheng Li, Lei Wu

One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity has played a crucial role in understanding important phenomena in deep learning. In this paper, we conduct a fine-grained analysis of this connectivity phenomenon. First, we demonstrate that in the overparameterized case, the connecting path can be as simple as a two-piece linear path, and the path length can be nearly equal to the Euclidean distance. This finding suggests that the landscape should be nearly convex in a certain sense. Second, we uncover a surprising star-shaped connectivity: For a finite number of typical minima, there exists a center on minima manifold that connects all of them simultaneously via linear paths. These results are provably valid for linear networks and two-layer ReLU networks under a teacher-student setup, and are empirically supported by models trained on MNIST and CIFAR-10.

Keyao Zhan, Puheng Li, Lei Wu

It was empirically observed in Entezari et al. (2021) that when accounting for the permutation invariance of neural networks, there is likely no loss barrier along the linear interpolation between two SGD solutions -- a phenomenon known as linear mode connectivity (LMC) modulo permutation. This phenomenon has sparked significant attention due to both its theoretical interest and practical relevance in applications such as model merging. In this paper, we provide a fine-grained analysis of this phenomenon for two-layer ReLU networks under a teacher-student setup. We show that as the student network width $m$ increases, the LMC loss barrier modulo permutation exhibits a double descent behavior. Particularly, when $m$ is sufficiently large, the barrier decreases to zero at a rate $O(m^{-1/2})$. Notably, this rate does not suffer from the curse of dimensionality and demonstrates how substantial permutation can reduce the LMC loss barrier. Moreover, we observe a sharp transition in the sparsity of GD/SGD solutions when increasing the learning rate and investigate how this sparsity preference affects the LMC loss barrier modulo permutation. Experiments on both synthetic and MNIST datasets corroborate our theoretical predictions and reveal a similar trend for more complex network architectures.

Jiaqi Han, Haotian Ye, Puheng Li et al.

Diffusion-based generative models have become dominant generators of high-fidelity images and videos but remain limited by their computationally expensive inference procedures. Existing acceleration techniques either require extensive model retraining or compromise significantly on sample quality. This paper explores a general, training-free, and model-agnostic acceleration strategy via multi-core parallelism. Our framework views multi-core diffusion sampling as an ODE solver pipeline, where slower yet accurate solvers progressively rectify faster solvers through a theoretically justified inter-core communication mechanism. This motivates our multi-core training-free diffusion sampling accelerator, CHORDS, which is compatible with various diffusion samplers, model architectures, and modalities. Through extensive experiments, CHORDS significantly accelerates sampling across diverse large-scale image and video diffusion models, yielding up to 2.1x speedup with four cores, improving by 50% over baselines, and 2.9x speedup with eight cores, all without quality degradation. This advancement enables CHORDS to establish a solid foundation for real-time, high-fidelity diffusion generation.