Chongxuan Li

Xiangming Gu, Chao Du, Tianyu Pang et al. · tsinghua

Due to their capacity to generate novel and high-quality samples, diffusion models have attracted significant research interest in recent years. Notably, the typical training objective of diffusion models, i.e., denoising score matching, has a closed-form optimal solution that can only generate training data replicating samples. This indicates that a memorization behavior is theoretically expected, which contradicts the common generalization ability of state-of-the-art diffusion models, and thus calls for a deeper understanding. Looking into this, we first observe that memorization behaviors tend to occur on smaller-sized datasets, which motivates our definition of effective model memorization (EMM), a metric measuring the maximum size of training data at which a learned diffusion model approximates its theoretical optimum. Then, we quantify the impact of the influential factors on these memorization behaviors in terms of EMM, focusing primarily on data distribution, model configuration, and training procedure. Besides comprehensive empirical results identifying the influential factors, we surprisingly find that conditioning training data on uninformative random labels can significantly trigger the memorization in diffusion models. Our study holds practical significance for diffusion model users and offers clues to theoretical research in deep generative models. Code is available at https://github.com/sail-sg/DiffMemorize.

Hanzhong Guo, Cheng Lu, Fan Bao et al. · tsinghua

Recently, diffusion models have achieved great success in generative tasks. Sampling from diffusion models is equivalent to solving the reverse diffusion stochastic differential equations (SDEs) or the corresponding probability flow ordinary differential equations (ODEs). In comparison, SDE-based solvers can generate samples of higher quality and are suited for image translation tasks like stroke-based synthesis. During inference, however, existing SDE-based solvers are severely constrained by the efficiency-effectiveness dilemma. Our investigation suggests that this is because the Gaussian assumption in the reverse transition kernel is frequently violated (even in the case of simple mixture data) given a limited number of discretization steps. To overcome this limitation, we introduce a novel class of SDE-based solvers called \emph{Gaussian Mixture Solvers (GMS)} for diffusion models. Our solver estimates the first three-order moments and optimizes the parameters of a Gaussian mixture transition kernel using generalized methods of moments in each step during sampling. Empirically, our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis in various diffusion models, which validates the motivation and effectiveness of GMS. Our code is available at https://github.com/Guohanzhong/GMS.

Cheng Lu, Yuhao Zhou, Fan Bao et al.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a $4\sim 16\times$ speedup compared with previous state-of-the-art training-free samplers on various datasets.

Cheng Lu, Yuhao Zhou, Fan Bao et al.

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

Yong Zhong, Hongtao Liu, Xiaodong Liu et al.

Deep generative models (DGMs) are data-eager because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the classical perspective of the bias-variance tradeoff, we propose regularized deep generative model (Reg-DGM), which leverages a nontransferable pre-trained model to reduce the variance of generative modeling with limited data. Formally, Reg-DGM optimizes a weighted sum of a certain divergence and the expectation of an energy function, where the divergence is between the data and the model distributions, and the energy function is defined by the pre-trained model w.r.t. the model distribution. We analyze a simple yet representative Gaussian-fitting case to demonstrate how the weighting hyperparameter trades off the bias and the variance. Theoretically, we characterize the existence and the uniqueness of the global minimum of Reg-DGM in a non-parametric setting and prove its convergence with neural networks trained by gradient-based methods. Empirically, with various pre-trained feature extractors and a data-dependent energy function, Reg-DGM consistently improves the generation performance of strong DGMs with limited data and achieves competitive results to the state-of-the-art methods. Our implementation is available at https://github.com/ML-GSAI/Reg-ADA-APA.

Cheng Lu, Huayu Chen, Jianfei Chen et al.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

Cheng Lu, Kaiwen Zheng, Fan Bao et al.

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE ("score-based diffusion ODE") for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.

Chendong Xiang, Fan Bao, Chongxuan Li et al.

Large-scale diffusion models like Stable Diffusion are powerful and find various real-world applications while customizing such models by fine-tuning is both memory and time inefficient. Motivated by the recent progress in natural language processing, we investigate parameter-efficient tuning in large diffusion models by inserting small learnable modules (termed adapters). In particular, we decompose the design space of adapters into orthogonal factors -- the input position, the output position as well as the function form, and perform Analysis of Variance (ANOVA), a classical statistical approach for analyzing the correlation between discrete (design options) and continuous variables (evaluation metrics). Our analysis suggests that the input position of adapters is the critical factor influencing the performance of downstream tasks. Then, we carefully study the choice of the input position, and we find that putting the input position after the cross-attention block can lead to the best performance, validated by additional visualization analyses. Finally, we provide a recipe for parameter-efficient tuning in diffusion models, which is comparable if not superior to the fully fine-tuned baseline (e.g., DreamBooth) with only 0.75 \% extra parameters, across various customized tasks.

Yidong Ouyang, Liyan Xie, Chongxuan Li et al.

The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in various real-world applications, including healthcare and finance, particularly when dealing with tabular datasets. This work presents a unified and principled diffusion-based framework for learning from data with missing values under various missing mechanisms. We first observe that the widely adopted "impute-then-generate" pipeline may lead to a biased learning objective. Then we propose to mask the regression loss of Denoising Score Matching in the training phase. We prove the proposed method is consistent in learning the score of data distributions, and the proposed training objective serves as an upper bound for the negative likelihood in certain cases. The proposed framework is evaluated on multiple tabular datasets using realistic and efficacious metrics and is demonstrated to outperform state-of-the-art diffusion model on tabular data with "impute-then-generate" pipeline by a large margin.

Jingyang Ou, Jiaqi Han, Minkai Xu et al.

Reinforcement Learning (RL) has proven highly effective for autoregressive language models, but adapting these methods to diffusion large language models (dLLMs) presents fundamental challenges. The core difficulty lies in likelihood approximation: while autoregressive models naturally provide token-level conditional probabilities essential for token-level RL objectives (e.g., GRPO), dLLMs generate sequences through iterative non-autoregressive denoising steps that lack this factorization. To address this fundamental mismatch, we propose ELBO-based Sequence-level Policy Optimization (ESPO), a principled RL framework that treats entire sequence generation as a single action and uses the ELBO as a tractable sequence-level likelihood proxy. Our method incorporates per-token normalization of importance ratios and robust KL-divergence estimation to ensure stable large-scale training. Extensive experiments on mathematical reasoning, coding, and planning tasks demonstrate that ESPO significantly outperforms token-level baselines, achieving dramatic improvements of 20-40 points on the Countdown task, while maintaining consistent gains on math and coding benchmarks. Our approach establishes sequence-level optimization as a principled and empirically effective paradigm for RL in dLLMs. Our code is available at https://github.com/ML-GSAI/ESPO.

Siyu Wang, Jianfei Chen, Chongxuan Li et al.

By applying entropy codecs with learned data distributions, neural compressors have significantly outperformed traditional codecs in terms of compression ratio. However, the high inference latency of neural networks hinders the deployment of neural compressors in practical applications. In this work, we propose Integer-only Discrete Flows (IODF), an efficient neural compressor with integer-only arithmetic. Our work is built upon integer discrete flows, which consists of invertible transformations between discrete random variables. We propose efficient invertible transformations with integer-only arithmetic based on 8-bit quantization. Our invertible transformation is equipped with learnable binary gates to remove redundant filters during inference. We deploy IODF with TensorRT on GPUs, achieving 10x inference speedup compared to the fastest existing neural compressors, while retaining the high compression rates on ImageNet32 and ImageNet64.

Min Zhao, Bokai Yan, Xue Yang et al.

Recent image diffusion transformers achieve high-fidelity generation, but struggle to generate images beyond these scales, suffering from content repetition and quality degradation. In this work, we present UltraImage, a principled framework that addresses both issues. Through frequency-wise analysis of positional embeddings, we identify that repetition arises from the periodicity of the dominant frequency, whose period aligns with the training resolution. We introduce a recursive dominant frequency correction to constrain it within a single period after extrapolation. Furthermore, we find that quality degradation stems from diluted attention and thus propose entropy-guided adaptive attention concentration, which assigns higher focus factors to sharpen local attention for fine detail and lower ones to global attention patterns to preserve structural consistency. Experiments show that UltraImage consistently outperforms prior methods on Qwen-Image and Flux (around 4K) across three generation scenarios, reducing repetition and improving visual fidelity. Moreover, UltraImage can generate images up to 6K*6K without low-resolution guidance from a training resolution of 1328p, demonstrating its extreme extrapolation capability. Project page is available at \href{https://thu-ml.github.io/ultraimage.github.io/}{https://thu-ml.github.io/ultraimage.github.io/}.

Shen Nie, Fengqi Zhu, Chao Du et al.

Masked diffusion models (MDMs) have shown promise in language modeling, yet their scalability and effectiveness in core language tasks, such as text generation and language understanding, remain underexplored. This paper establishes the first scaling law for MDMs, demonstrating a scaling rate comparable to autoregressive models (ARMs) and a relatively small compute gap. Motivated by their scalability, we train a family of MDMs with up to 1.1 billion (B) parameters to systematically evaluate their performance against ARMs of comparable or larger sizes. Fully leveraging the probabilistic formulation of MDMs, we propose a simple yet effective unsupervised classifier-free guidance that effectively exploits large-scale unpaired data, boosting performance for conditional inference. In language understanding, the 1.1B MDM outperforms the 1.1B TinyLlama model trained on the same data across four of eight zero-shot benchmarks. Notably, it achieves competitive math reasoning ability with the 7B Llama-2 model on the GSM8K dataset. In text generation, MDMs with 16 times more pre-training time offer a flexible trade-off against ARMs with the accelerated sampling technique KV-Cache: MDMs match ARMs in performance while being 1.4 times faster during sampling. Moreover, MDMs address challenging tasks for ARMs by effectively handling bidirectional reasoning and adapting to temporal shifts in data. Notably, a 1.1B MDM breaks the reverse curse encountered by much larger ARMs with significantly more data and computation, such as 13B Llama-2 and 175B GPT-3. Our code is available at https://github.com/ML-GSAI/SMDM.

Siqi Kou, Lei Gan, Dequan Wang et al.

Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a pixel-wise uncertainty estimator for generations from diffusion models based on Bayesian inference. In particular, we derive a novel uncertainty iteration principle to characterize the uncertainty dynamics in diffusion, and leverage the last-layer Laplace approximation for efficient Bayesian inference. The estimated pixel-wise uncertainty can not only be aggregated into a sample-wise metric to filter out low-fidelity images but also aids in augmenting successful generations and rectifying artifacts in failed generations in text-to-image tasks. Extensive experiments demonstrate the efficacy of BayesDiff and its promise for practical applications.

Xiangxin Zhou, Zichen Liu, Anya Sims et al.

The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.

Kaiwen Xue, Yuhao Zhou, Shen Nie et al.

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN's regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e.g., 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of 5~20 times for free. Our code is available at https://github.com/ML-GSAI/BFN-Solver.

Rui-Jie Zhu, Tianhao Peng, Tianhao Cheng et al.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

Yijing Liu, Chao Du, Tianyu Pang et al. · tsinghua

Recent research has made significant progress in optimizing diffusion models for downstream objectives, which is an important pursuit in fields such as graph generation for drug design. However, directly applying these models to graph presents challenges, resulting in suboptimal performance. This paper introduces graph diffusion policy optimization (GDPO), a novel approach to optimize graph diffusion models for arbitrary (e.g., non-differentiable) objectives using reinforcement learning. GDPO is based on an eager policy gradient tailored for graph diffusion models, developed through meticulous analysis and promising improved performance. Experimental results show that GDPO achieves state-of-the-art performance in various graph generation tasks with complex and diverse objectives. Code is available at https://github.com/sail-sg/GDPO.

Shen Nie, Fengqi Zhu, Zebin You et al.

The capabilities of large language models (LLMs) are widely regarded as relying on autoregressive models (ARMs). We challenge this notion by introducing LLaDA, a diffusion model trained from scratch under the pre-training and supervised fine-tuning (SFT) paradigm. LLaDA employs a forward data masking process and a reverse generation process, parameterized by a Transformer to predict masked tokens. It provides a principled generative approach for probabilistic inference by optimizing a likelihood lower bound. Across extensive benchmarks on general tasks, math, code, and so on, LLaDA demonstrates strong scalability and performs comparably to our self-constructed ARM baselines. Remarkably, LLaDA 8B is competitive with strong LLMs like LLaMA3 8B in in-context learning and, after SFT, exhibits impressive instruction-following abilities in case studies such as multi-turn dialogue. Moreover, LLaDA addresses the reversal curse, surpassing GPT-4o in a reversal poem completion task. Our findings show the promise of diffusion models for language modeling at scale and challenge the common assumption that core LLM capabilities discussed above inherently depend on ARMs. Project page and codes: https://ml-gsai.github.io/LLaDA-demo/.

Zhengyi Wang, Yikai Wang, Yifei Chen et al.

Feed-forward 3D generative models like the Large Reconstruction Model (LRM) have demonstrated exceptional generation speed. However, the transformer-based methods do not leverage the geometric priors of the triplane component in their architecture, often leading to sub-optimal quality given the limited size of 3D data and slow training. In this work, we present the Convolutional Reconstruction Model (CRM), a high-fidelity feed-forward single image-to-3D generative model. Recognizing the limitations posed by sparse 3D data, we highlight the necessity of integrating geometric priors into network design. CRM builds on the key observation that the visualization of triplane exhibits spatial correspondence of six orthographic images. First, it generates six orthographic view images from a single input image, then feeds these images into a convolutional U-Net, leveraging its strong pixel-level alignment capabilities and significant bandwidth to create a high-resolution triplane. CRM further employs Flexicubes as geometric representation, facilitating direct end-to-end optimization on textured meshes. Overall, our model delivers a high-fidelity textured mesh from an image in just 10 seconds, without any test-time optimization.

Jingyang Ou, Shen Nie, Kaiwen Xue et al.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval, which enables sampling acceleration. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Min Zhao, Rongzhen Wang, Fan Bao et al.

This paper presents \emph{ControlVideo} for text-driven video editing -- generating a video that aligns with a given text while preserving the structure of the source video. Building on a pre-trained text-to-image diffusion model, ControlVideo enhances the fidelity and temporal consistency by incorporating additional conditions (such as edge maps), and fine-tuning the key-frame and temporal attention on the source video-text pair via an in-depth exploration of the design space. Extensive experimental results demonstrate that ControlVideo outperforms various competitive baselines by delivering videos that exhibit high fidelity w.r.t. the source content, and temporal consistency, all while aligning with the text. By incorporating Low-rank adaptation layers into the model before training, ControlVideo is further empowered to generate videos that align seamlessly with reference images. More importantly, ControlVideo can be readily extended to the more challenging task of long video editing (e.g., with hundreds of frames), where maintaining long-range temporal consistency is crucial. To achieve this, we propose to construct a fused ControlVideo by applying basic ControlVideo to overlapping short video segments and key frame videos and then merging them by pre-defined weight functions. Empirical results validate its capability to create videos across 140 frames, which is approximately 5.83 to 17.5 times more than what previous works achieved. The code is available at \href{https://github.com/thu-ml/controlvideo}{https://github.com/thu-ml/controlvideo} and the visualization results are available at \href{https://drive.google.com/file/d/1wEgc2io3UwmoC5vTPbkccFvTkwVqsZlK/view?usp=drive_link}{HERE}.

Yunqing Zhao, Tianyu Pang, Chao Du et al.

Large vision-language models (VLMs) such as GPT-4 have achieved unprecedented performance in response generation, especially with visual inputs, enabling more creative and adaptable interaction than large language models such as ChatGPT. Nonetheless, multimodal generation exacerbates safety concerns, since adversaries may successfully evade the entire system by subtly manipulating the most vulnerable modality (e.g., vision). To this end, we propose evaluating the robustness of open-source large VLMs in the most realistic and high-risk setting, where adversaries have only black-box system access and seek to deceive the model into returning the targeted responses. In particular, we first craft targeted adversarial examples against pretrained models such as CLIP and BLIP, and then transfer these adversarial examples to other VLMs such as MiniGPT-4, LLaVA, UniDiffuser, BLIP-2, and Img2Prompt. In addition, we observe that black-box queries on these VLMs can further improve the effectiveness of targeted evasion, resulting in a surprisingly high success rate for generating targeted responses. Our findings provide a quantitative understanding regarding the adversarial vulnerability of large VLMs and call for a more thorough examination of their potential security flaws before deployment in practice. Code is at https://github.com/yunqing-me/AttackVLM.

Fengqi Zhu, Rongzhen Wang, Shen Nie et al.

While Masked Diffusion Models (MDMs), such as LLaDA, present a promising paradigm for language modeling, there has been relatively little effort in aligning these models with human preferences via reinforcement learning. The challenge primarily arises from the high variance in Evidence Lower Bound (ELBO)-based likelihood estimates required for preference optimization. To address this issue, we propose Variance-Reduced Preference Optimization (VRPO), a framework that formally analyzes the variance of ELBO estimators and derives bounds on both the bias and variance of preference optimization gradients. Building on this theoretical foundation, we introduce unbiased variance reduction strategies, including optimal Monte Carlo budget allocation and antithetic sampling, that significantly improve the performance of MDM alignment. We demonstrate the effectiveness of VRPO by applying it to LLaDA, and the resulting model, LLaDA 1.5, outperforms its SFT-only predecessor consistently and significantly across mathematical (GSM8K +4.7), code (HumanEval +3.0, MBPP +1.8), and alignment benchmarks (IFEval +4.0, Arena-Hard +4.3). Furthermore, LLaDA 1.5 demonstrates a highly competitive mathematical performance compared to strong language MDMs and ARMs. Project page: https://ml-gsai.github.io/LLaDA-1.5-Demo/.

Zebin You, Shen Nie, Xiaolu Zhang et al.

In this work, we introduce LLaDA-V, a purely diffusion-based Multimodal Large Language Model (MLLM) that integrates visual instruction tuning with masked diffusion models, representing a departure from the autoregressive paradigms dominant in current multimodal approaches. Built upon LLaDA, a representative large language diffusion model, LLaDA-V incorporates a vision encoder and MLP connector that projects visual features into the language embedding space, enabling effective multimodal alignment. Our empirical investigation reveals several intriguing results: First, LLaDA-V demonstrates promising multimodal performance despite its language model being weaker on purely textual tasks than counterparts like LLaMA3-8B and Qwen2-7B. When trained on the same instruction data, LLaDA-V is highly competitive to LLaMA3-V across multimodal tasks with better data scalability. It also narrows the performance gap to Qwen2-VL, suggesting the effectiveness of its architecture for multimodal tasks. Second, LLaDA-V achieves state-of-the-art performance in multimodal understanding compared to existing hybrid autoregressive-diffusion and purely diffusion-based MLLMs. Our findings suggest that large language diffusion models show promise in multimodal contexts and warrant further investigation in future research. Project page and codes: https://ml-gsai.github.io/LLaDA-V-demo/.

Juntu Zhao, Jialing Zhang, Chongxuan Li et al.

Recent closed-source multimodal systems have made great advances, but their hidden language for understanding the world remains opaque because of their black-box architectures. In this paper, we use the systems' preference bias to study their hidden language: During the process of compressing the input images (typically containing multiple concepts) into texts and then reconstructing them into images, the systems' inherent preference bias introduces specific shifts in the outputs, disrupting the original input concept co-occurrence. We employ the multi-round "telephone game" to strategically leverage this bias. By observing the co-occurrence frequencies of concepts in telephone games, we quantitatively investigate the concept connection strength in the understanding of multimodal systems, i.e., "hidden language." We also contribute Telescope, a dataset of 10,000+ concept pairs, as the database of our telephone game framework. Our telephone game is test-time scalable: By iteratively running telephone games, we can construct a global map of concept connections in multimodal systems' understanding. Here we can identify preference bias inherited from training, assess generalization capability advancement, and discover more stable pathways for fragile concept connections. Furthermore, we use Reasoning-LLMs to uncover unexpected concept relationships that transcend textual and visual similarities, inferring how multimodal systems understand and simulate the world. This study offers a new perspective on the hidden language of multimodal systems and lays the foundation for future research on the interpretability and controllability of multimodal systems.

Luxi Chen, Zihan Zhou, Min Zhao et al.

Generating flexible-view 3D scenes, including 360° rotation and zooming, from single images is challenging due to a lack of 3D data. To this end, we introduce FlexWorld, a novel framework consisting of two key components: (1) a strong video-to-video (V2V) diffusion model to generate high-quality novel view images from incomplete input rendered from a coarse scene, and (2) a progressive expansion process to construct a complete 3D scene. In particular, leveraging an advanced pre-trained video model and accurate depth-estimated training pairs, our V2V model can generate novel views under large camera pose variations. Building upon it, FlexWorld progressively generates new 3D content and integrates it into the global scene through geometry-aware scene fusion. Extensive experiments demonstrate the effectiveness of FlexWorld in generating high-quality novel view videos and flexible-view 3D scenes from single images, achieving superior visual quality under multiple popular metrics and datasets compared to existing state-of-the-art methods. Qualitatively, we highlight that FlexWorld can generate high-fidelity scenes with flexible views like 360° rotations and zooming. Project page: https://ml-gsai.github.io/FlexWorld.

Fengqi Zhu, Zebin You, Yipeng Xing et al.

We introduce LLaDA-MoE, a large language diffusion model with the Mixture-of-Experts (MoE) architecture, trained from scratch on approximately 20T tokens. LLaDA-MoE achieves competitive performance with significantly reduced computational overhead by maintaining a 7B-parameter capacity while activating only 1.4B parameters during inference. Our empirical evaluation reveals that LLaDA-MoE achieves state-of-the-art performance among diffusion language models with larger parameters, surpassing previous diffusion language models LLaDA, LLaDA 1.5, and Dream across multiple benchmarks. The instruct-tuned model LLaDA-MoE-7B-A1B-Instruct demonstrates capabilities comparable to Qwen2.5-3B-Instruct in knowledge understanding, code generation, mathematical reasoning, agent and alignment tasks, despite using fewer active parameters. Our results show that integrating a sparse MoE architecture into the training objective of masked diffusion language models still brings out MoE's strengths under efficient inference with few active parameters, and opens ample room for further exploration of diffusion language models. LLaDA-MoE models are available at Huggingface.

Guangxin He, Shen Nie, Fengqi Zhu et al.

Diffusion LLMs have attracted growing interest, with plenty of recent work emphasizing their great potential in various downstream tasks; yet the long-context behavior of diffusion LLMs remains largely uncharted. We present a case study of post-training techniques for extending the context window of diffusion LLMs (i.e., LLaDA) without retraining from scratch. We show that a simple modification to the standard Rotary Positional Embeddings (RoPE) extension effectively accommodates the probabilistic modeling inherent in the diffusion process, enabling stable scaling to longer context ranges. We further compare masking strategies used during post-training and analyze their impact on optimization stability and long-range recall. Instantiating these insights, we introduce UltraLLaDA, a diffusion LLM with a 128K-token context window that, in our empirical evaluation on long-context tasks, significantly outperforms training-free baselines. Our experimental results highlight the special positional extension as a key lever for scaling diffusion LLMs to extended contexts and offer practical guidance for practitioners seeking 128K-scale context via efficient post-training.

Chenyu Zheng, Xinyu Zhang, Rongzhen Wang et al.

Diffusion Transformers have emerged as the foundation for vision generative models, but their scalability is limited by the high cost of hyperparameter (HP) tuning at large scales. Recently, Maximal Update Parametrization ($μ$P) was proposed for vanilla Transformers, which enables stable HP transfer from small to large language models, and dramatically reduces tuning costs. However, it remains unclear whether $μ$P of vanilla Transformers extends to diffusion Transformers, which differ architecturally and objectively. In this work, we generalize standard $μ$P to diffusion Transformers and validate its effectiveness through large-scale experiments. First, we rigorously prove that $μ$P of mainstream diffusion Transformers, including U-ViT, DiT, PixArt-$α$, and MMDiT, aligns with that of the vanilla Transformer, enabling the direct application of existing $μ$P methodologies. Leveraging this result, we systematically demonstrate that DiT-$μ$P enjoys robust HP transferability. Notably, DiT-XL-2-$μ$P with transferred learning rate achieves 2.9 times faster convergence than the original DiT-XL-2. Finally, we validate the effectiveness of $μ$P on text-to-image generation by scaling PixArt-$α$ from 0.04B to 0.61B and MMDiT from 0.18B to 18B. In both cases, models under $μ$P outperform their respective baselines while requiring small tuning cost, only 5.5% of one training run for PixArt-$α$ and 3% of consumption by human experts for MMDiT-18B. These results establish $μ$P as a principled and efficient framework for scaling diffusion Transformers.

Hanzhong Guo, Shen Nie, Chao Du et al.

Personalized generative diffusion models, capable of synthesizing highly realistic images based on a few reference portraits, may pose substantial social, ethical, and legal risks via identity replication. Existing defense mechanisms rely on computationally intensive adversarial perturbations tailored to individual images, rendering them impractical for real-world deployment. This study introduces the Real-time Identity Defender (RID), a neural network designed to generate adversarial perturbations through a single forward pass, bypassing the need for image-specific optimization. RID achieves unprecedented efficiency, with defense times as low as 0.12 seconds on a single NVIDIA A100 80G GPU (4,400 times faster than leading methods) and 1.1 seconds per image on a standard Intel i9 CPU, making it suitable for edge devices such as smartphones. Despite its efficiency, RID achieves promising protection performance across visual and quantitative benchmarks, effectively mitigating identity replication risks. Our analysis reveals that RID's perturbations mimic the efficacy of traditional defenses while exhibiting properties distinct from natural noise, such as Gaussian perturbations. To enhance robustness, we extend RID into an ensemble framework that integrates multiple pre-trained text-to-image diffusion models, ensuring resilience against black-box attacks and post-processing techniques, including image compression and purification. Our model is envisioned to play a crucial role in safeguarding portrait rights, thereby preventing illegal and unethical uses.

Jia-Nan Li, Jian Guan, Wei Wu et al.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce \textsc{ReFusion}, a novel masked diffusion model that integrates sequence reorganization into the causal attention framework. By elevating parallel decoding from the token level to a higher slot level, \textsc{ReFusion} interleaves inter-slot diffusion-based selection with intra-slot autoregressive infilling, while reordering newly generated slots ahead of the remaining masks after each iteration. Consequently, this design simultaneously unlocks full KV cache reuse and reduces learning complexity from an intractable token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that \textsc{ReFusion} not only overwhelmingly surpasses prior MDMs with a 34\% performance gain and an over 18$\times$ speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 2.33$\times$ average speedup.

Min Zhao, Hongzhou Zhu, Yingze Wang et al.

Despite advances, video diffusion transformers still struggle to generalize beyond their training length, a challenge we term video length extrapolation. We identify two failure modes: model-specific periodic content repetition and a universal quality degradation. Prior works attempt to solve repetition via positional encodings, overlooking quality degradation and achieving only limited extrapolation. In this paper, we revisit this challenge from a more fundamental view: attention maps, which directly govern how context influences outputs. We identify that both failure modes arise from a unified cause: attention dispersion, where tokens beyond the training window dilute learned attention patterns. This leads to quality degradation and repetition emerges as a special case when this dispersion becomes structured into periodic attention patterns, induced by harmonic properties of positional encodings. Building on this insight, we propose UltraViCo, a training-free, plug-and-play method that suppresses attention for tokens beyond the training window via a constant decay factor. By jointly addressing both failure modes, we outperform a broad set of baselines largely across models and extrapolation ratios, pushing the extrapolation limit from 2x to 4x. Remarkably, it improves Dynamic Degree and Imaging Quality by 233% and 40.5% over the previous best method at 4x extrapolation. Furthermore, our method generalizes seamlessly to downstream tasks such as controllable video synthesis and editing.

Sitong Chen, Shen Nie, Jiacheng Sun et al.

We present a systematic theoretical framework that interprets masked diffusion models (MDMs) as solutions to energy minimization problems in discrete optimal transport. Specifically, we prove that three distinct energy formulations--kinetic, conditional kinetic, and geodesic energy--are mathematically equivalent under the structure of MDMs, and that MDMs minimize all three when the mask schedule satisfies a closed-form optimality condition. This unification not only clarifies the theoretical foundations of MDMs, but also motivates practical improvements in sampling. By parameterizing interpolation schedules via Beta distributions, we reduce the schedule design space to a tractable 2D search, enabling efficient post-training tuning without model modification. Experiments on synthetic and real-world benchmarks demonstrate that our energy-inspired schedules outperform hand-crafted baselines, particularly in low-step sampling settings.

Min Zhao, Hongzhou Zhu, Chendong Xiang et al.

Diffusion models have obtained substantial progress in image-to-video generation. However, in this paper, we find that these models tend to generate videos with less motion than expected. We attribute this to the issue called conditional image leakage, where the image-to-video diffusion models (I2V-DMs) tend to over-rely on the conditional image at large time steps. We further address this challenge from both inference and training aspects. First, we propose to start the generation process from an earlier time step to avoid the unreliable large-time steps of I2V-DMs, as well as an initial noise distribution with optimal analytic expressions (Analytic-Init) by minimizing the KL divergence between it and the actual marginal distribution to bridge the training-inference gap. Second, we design a time-dependent noise distribution (TimeNoise) for the conditional image during training, applying higher noise levels at larger time steps to disrupt it and reduce the model's dependency on it. We validate these general strategies on various I2V-DMs on our collected open-domain image benchmark and the UCF101 dataset. Extensive results show that our methods outperform baselines by producing higher motion scores with lower errors while maintaining image alignment and temporal consistency, thereby yielding superior overall performance and enabling more accurate motion control. The project page: \url{https://cond-image-leak.github.io/}.

Zhengyi Wang, Cheng Lu, Yikai Wang et al.

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present variational score distillation (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i.e., $7.5$). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed ProlificDreamer, can generate high rendering resolution (i.e., $512\times512$) and high-fidelity NeRF with rich structure and complex effects (e.g., smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic. Project page and codes: https://ml.cs.tsinghua.edu.cn/prolificdreamer/

Guoqiang Wu, Chongxuan Li, Yilong Yin

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w.r.t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: \emph{the label-wise class imbalance}. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

Liyuan Wang, Xingxing Zhang, Kuo Yang et al.

Continual learning needs to overcome catastrophic forgetting of the past. Memory replay of representative old training samples has been shown as an effective solution, and achieves the state-of-the-art (SOTA) performance. However, existing work is mainly built on a small memory buffer containing a few original data, which cannot fully characterize the old data distribution. In this work, we propose memory replay with data compression (MRDC) to reduce the storage cost of old training samples and thus increase their amount that can be stored in the memory buffer. Observing that the trade-off between the quality and quantity of compressed data is highly nontrivial for the efficacy of memory replay, we propose a novel method based on determinantal point processes (DPPs) to efficiently determine an appropriate compression quality for currently-arrived training samples. In this way, using a naive data compression algorithm with a properly selected quality can largely boost recent strong baselines by saving more compressed data in a limited storage space. We extensively validate this across several benchmarks of class-incremental learning and in a realistic scenario of object detection for autonomous driving.

Fan Bao, Chongxuan Li, Jun Zhu et al.

Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference is to estimate the variance in each timestep of the reverse process. In this work, we present a surprising result that both the optimal reverse variance and the corresponding optimal KL divergence of a DPM have analytic forms w.r.t. its score function. Building upon it, we propose Analytic-DPM, a training-free inference framework that estimates the analytic forms of the variance and KL divergence using the Monte Carlo method and a pretrained score-based model. Further, to correct the potential bias caused by the score-based model, we derive both lower and upper bounds of the optimal variance and clip the estimate for a better result. Empirically, our analytic-DPM improves the log-likelihood of various DPMs, produces high-quality samples, and meanwhile enjoys a 20x to 80x speed up.

Fan Bao, Guoqiang Wu, Chongxuan Li et al.

The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the analysis on generalization largely open. This paper attempts to address the issue by presenting an expectation bound w.r.t. the validation set based on uniform stability. Our results can explain some mysterious behaviours of the bilevel programming in practice, for instance, overfitting to the validation set. We also present an expectation bound for the classical cross-validation algorithm. Our results suggest that gradient-based algorithms can be better than cross-validation under certain conditions in a theoretical perspective. Furthermore, we prove that regularization terms in both the outer and inner levels can relieve the overfitting problem in gradient-based algorithms. In experiments on feature learning and data reweighting for noisy labels, we corroborate our theoretical findings.

Guoqiang Wu, Chongxuan Li, Kun Xu et al.

(Partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical work on multi-label ranking mainly focuses on (Fisher) consistency analyses. However, there is a gap between existing theory and practice -- some pairwise losses can lead to promising performance but lack consistency, while some univariate losses are consistent but usually have no clear superiority in practice. In this paper, we attempt to fill this gap through a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. Our results show that learning algorithms with the consistent univariate loss have an error bound of $O(c)$ ($c$ is the number of labels), while algorithms with the inconsistent pairwise loss depend on $O(\sqrt{c})$ as shown in prior work. This explains that the latter can achieve better performance than the former in practice. Moreover, we present an inconsistent reweighted univariate loss-based learning algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results validate our theoretical analyses.

Tsung Wei Tsai, Chongxuan Li, Jun Zhu

We present Mixture of Contrastive Experts (MiCE), a unified probabilistic clustering framework that simultaneously exploits the discriminative representations learned by contrastive learning and the semantic structures captured by a latent mixture model. Motivated by the mixture of experts, MiCE employs a gating function to partition an unlabeled dataset into subsets according to the latent semantics and multiple experts to discriminate distinct subsets of instances assigned to them in a contrastive learning manner. To solve the nontrivial inference and learning problems caused by the latent variables, we further develop a scalable variant of the Expectation-Maximization (EM) algorithm for MiCE and provide proof of the convergence. Empirically, we evaluate the clustering performance of MiCE on four widely adopted natural image datasets. MiCE achieves significantly better results than various previous methods and a strong contrastive learning baseline.

Cheng Lu, Jianfei Chen, Chongxuan Li et al.

Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing flows by allowing the mapping to be implicitly defined by the roots of an equation $F(\boldsymbol{\mathbf{z}}, \boldsymbol{\mathbf{x}})= \boldsymbol{\mathbf{0}}$. ImpFlows build on residual flows (ResFlows) with a proper balance between expressiveness and tractability. Through theoretical analysis, we show that the function space of ImpFlow is strictly richer than that of ResFlows. Furthermore, for any ResFlow with a fixed number of blocks, there exists some function that ResFlow has a non-negligible approximation error. However, the function is exactly representable by a single-block ImpFlow. We propose a scalable algorithm to train and draw samples from ImpFlows. Empirically, we evaluate ImpFlow on several classification and density modeling tasks, and ImpFlow outperforms ResFlow with a comparable amount of parameters on all the benchmarks.

Qijun Luo, Zhili Liu, Lanqing Hong et al.

Semi-supervised domain adaptation (SSDA), which aims to learn models in a partially labeled target domain with the assistance of the fully labeled source domain, attracts increasing attention in recent years. To explicitly leverage the labeled data in both domains, we naturally introduce a conditional GAN framework to transfer images without changing the semantics in SSDA. However, we identify a label-domination problem in such an approach. In fact, the generator tends to overlook the input source image and only memorizes prototypes of each class, which results in unsatisfactory adaptation performance. To this end, we propose a simple yet effective Relaxed conditional GAN (Relaxed cGAN) framework. Specifically, we feed the image without its label to our generator. In this way, the generator has to infer the semantic information of input data. We formally prove that its equilibrium is desirable and empirically validate its practical convergence and effectiveness in image transfer. Additionally, we propose several techniques to make use of unlabeled data in the target domain, enhancing the model in SSDA settings. We validate our method on the well-adopted datasets: Digits, DomainNet, and Office-Home. We achieve state-of-the-art performance on DomainNet, Office-Home and most digit benchmarks in low-resource and high-resource settings.

Liyuan Wang, Kuo Yang, Chongxuan Li et al.

Continual learning usually assumes the incoming data are fully labeled, which might not be applicable in real applications. In this work, we consider semi-supervised continual learning (SSCL) that incrementally learns from partially labeled data. Observing that existing continual learning methods lack the ability to continually exploit the unlabeled data, we propose deep Online Replay with Discriminator Consistency (ORDisCo) to interdependently learn a classifier with a conditional generative adversarial network (GAN), which continually passes the learned data distribution to the classifier. In particular, ORDisCo replays data sampled from the conditional generator to the classifier in an online manner, exploiting unlabeled data in a time- and storage-efficient way. Further, to explicitly overcome the catastrophic forgetting of unlabeled data, we selectively stabilize parameters of the discriminator that are important for discriminating the pairs of old unlabeled data and their pseudo-labels predicted by the classifier. We extensively evaluate ORDisCo on various semi-supervised learning benchmark datasets for SSCL, and show that ORDisCo achieves significant performance improvement on SVHN, CIFAR10 and Tiny-ImageNet, compared to strong baselines.

Fan Bao, Kun Xu, Chongxuan Li et al.

The learning and evaluation of energy-based latent variable models (EBLVMs) without any structural assumptions are highly challenging, because the true posteriors and the partition functions in such models are generally intractable. This paper presents variational estimates of the score function and its gradient with respect to the model parameters in a general EBLVM, referred to as VaES and VaGES respectively. The variational posterior is trained to minimize a certain divergence to the true model posterior and the bias in both estimates can be bounded by the divergence theoretically. With a minimal model assumption, VaES and VaGES can be applied to the kernelized Stein discrepancy (KSD) and score matching (SM)-based methods to learn EBLVMs. Besides, VaES can also be used to estimate the exact Fisher divergence between the data and general EBLVMs.

Fan Bao, Chongxuan Li, Kun Xu et al.

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

Tianyu Pang, Kun Xu, Chongxuan Li et al.

Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching (SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference (FD). Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations. Thus, it reduces the total computational cost while also improving numerical stability. We provide two instantiations by reformulating variants of SM objectives into the FD forms. Empirically, we demonstrate that our methods produce results comparable to the gradient-based counterparts while being much more computationally efficient.

Chongxuan Li, Kun Xu, Jiashuo Liu et al.

We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Under a nonparametric assumption, we prove the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player mechanism, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extreme low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on more than 10 benchmarks no matter data augmentation is applied or not.

Kun Xu, Chongxuan Li, Jun Zhu et al.

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the function space and provide simple yet effective methods to stabilize GANs' training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, where CLC is implemented as a squared $L2$ regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.