生成模型理论与方法

Diffusion large language models promise parallel token generation, yet inference remains bottlenecked by deciding which masked tokens can be safely committed together. Fast-dLLM addressed this with KV caching and confidence-guided parallel decoding, but its decoding theory uses a homogeneous high-confidence assumption that effectively reduces each candidate set to its weakest selected token. We argue that this leaves speed on the table because real decoding steps exhibit heterogeneous confidence profiles. We propose Fast-dLLM++, a training-free extension that introduces Fréchet profile decoding: selecting parallel commit sets from the full sorted confidence profile rather than a single worst-case confidence. The resulting rule is a heterogeneous-confidence generalization of Fast-dLLM's factor selector and it recovers the previous rule exactly in the equal-confidence case and adds a provable heterogeneity bonus when the selected tokens have uneven confidences. Fast-dLLM++ leaves the model, diffusion process, and cache implementation entirely unchanged, making it a drop-in replacement for existing Fast-dLLM decoding. Experiments on GSM8K, MATH, HumanEval, and MBPP with the LLaDA-8B model show that the theoretical improvement translates directly into empirical gains: profile-aware selection improves the accuracy--throughput frontier by exploiting safe parallelism that weakest-token rules miss, achieving up to 37% higher throughput at comparable accuracy. Our anonymous code release is at https://github.com/Ringo-Star/FastdLLM_plusplus.

Video diffusion models have significantly advanced portrait video generation, yet their high computational demands limit their use in interactive applications. This work presents a framework for streamable talking portrait video generation conditioned on speech audio and reference images. Designed meticulously for streaming scenarios, it features a causal video VAE for deep latent compression and an autoregressive latent denoising model. Our causal VAE integrates a variable number of reference images as guidance, allowing the network to focus on dynamic information rather than static appearance, thereby enhancing compression efficacy and reconstruction quality. Additionally, we extend the residual auto-encoding paradigm to improve spatial-temporal causality handling in our VAE. The generator is based on a Rectified Flow Transformer architecture and produces video latents in a blockwise auto-regressive manner. Our method enables the real-time generation of high-quality talking portrait videos, achieving speeds significantly faster than baseline models. Furthermore, comprehensive experiments demonstrate that it is on par with or even outperforms these large models in realism, vividness, and video quality.

Diffusion models have shown remarkable success in video generation. However, whether such models are truly aware of the 3D structure underlying visual observations, rather than simply reproducing plausible 2D projections, remains an open question. In this work, we investigate this question through human motion control, a task that requires precise modelling of 3D human geometry, motion, camera viewpoint, and scene context. Unlike prior methods that rely on rendered 2D motion guidance videos, we propose a render-free framework that conditions video generation directly on compressed 3D human mesh tokens. This representation preserves full 3D geometric information while enabling a unified token-based generation pipeline that processes video tokens jointly with motion tokens in a DiT-based architecture. This design requires the model to reason jointly about appearance, 3D structure, and camera viewpoint during video generation. Experimental results demonstrate strong performance on human motion control benchmarks, while reducing artifacts induced by view-dependent 2D guidance and trajectory-pose mismatches during editing. These findings suggest that video diffusion models, when equipped with mesh tokenization, can better capture complex 3D human structures and their interactions with the surrounding environment.

Bayesian inference provides a principled framework for modeling epistemic uncertainty in neural networks by treating predictions as distributions rather than deterministic values. Meanwhile, diffusion-based models for 3D molecular graph generation operate on fragile geometric structures governed by strict chemical constraints, making inference highly sensitive to uncertainty miscalibration. A largely overlooked issue is that epistemic uncertainty arising from the learned denoiser interacts with the aleatoric uncertainty intentionally injected during reverse diffusion, leading to systematic variance inflation and a mismatch between the true distribution and the simulated distribution. This effect is particularly detrimental for high-precision molecular generation, where even small deviations can violate chemical validity. In this work, we provide a theoretical and empirical analysis of how epistemic uncertainty propagates through diffusion inference and degrades sampling quality. Building on this investigation, we propose UCD (Uncertainty-Calibrated Diffusion), a simple yet effective method that calibrates the reverse diffusion process to account for epistemic uncertainty. Extensive experiments on standard 3D molecular benchmarks demonstrate that UCD consistently improves sampling quality across diverse baseline methods, establishing new state-of-the-art performance for 3D molecular diffusion. The code is available at https://github.com/jiuguaiwf/UCD.

In this work, we introduce a novel training-free inversion (TFinv) framework for one-step diffusion models,addressing key challenges in real image inversion and editing. We first identify two critical factors hamperingreal-image inversion and editing: (1) Initial Latent Editability, which is related to the distance between theinitial noise and the ideal Gaussian distribution, and (2) Caption Gap, which means the alignment betweentext captions and image representations. Both factors influence inversion efficiency and the editability ofone-step diffusion models. Then, we propose two novel techniques: iterative noise alignment (iterNA), whichminimizes the distribution gap to align with the normal Gaussian distribution, and suffix learning (suffL),which enhances text-to-image caption alignment by introducing learned suffix prompt tokens. These techniquesenable precise inversion of input images into their initial noise representations and facilitate image editing.Furthermore, we propose a mask-based editing technique for localized edits while preserving backgroundintegrity. Comprehensive experiments on the PIE-Bench dataset validate that our method TFinv not onlyachieves state-of-the-art performance in one-step diffusion editing, but also significantly outperforms existingmultistep approaches in efficiency. The code is available at https://github.com/tttao-uwu/TFinv.git.

We propose Decoupled Residual Denoising Diffusion models (DRDD) for unified and data-efficient image-to-image (I2I) translation. While diffusion models have advanced I2I translation in terms of quality and diversity, we uncover a previously under-explored property in diffusion models. Crucially, beyond its conventional role of manifold lifting (i.e., moving data off low-dimensional manifolds), injecting Gaussian noise facilitates domain harmonization by implicitly aligning feature distributions across domains, a property particularly advantageous for unified I2I translation. However, existing diffusion models prematurely erode this harmonization effect, as noise and residuals are simultaneously removed in a single coupled diffusion process. To address this, DRDD decouples the diffusion process into two sequential and independent diffusion stages: (1) a stochastic noise diffusion for domain harmonization and manifold lifting, and (2) a deterministic residual diffusion that learns the core semantic mapping entirely within the fixed-noise domain. This decoupling preserves harmonization and manifold lifting effects throughout the transformation, substantially simplifying the learning of unified mappings across diverse tasks and domains. Notably, the noise diffusion stage is trained exclusively on abundant, unpaired target-domain images, greatly improving data efficiency. Comprehensive theoretical and empirical analysis demonstrates that DRDD is broadly compatible with mainstream diffusion models and consistently delivers robust, unified I2I translation, even under limited paired data. Our code is available at https://github.com/HKU-HealthAI/DRDD.

Distribution Matching Distillation (DMD) is a widely used paradigm for accelerating inference in few-step video diffusion models. However, DMD-style video distillation faces two coupled challenges: the fake score must track a continuously evolving generator, making training costly when frequent updates are required, while reverse-KL-style matching can be mode-seeking and conservative for preserving strong motion dynamics. To address these issues, we propose Score Gradient Matching Distillation (SGMD). SGMD adopts a fake-score perspective by directly optimizing the fake score toward the teacher, while using teacher stop-gradient Fisher as a stable distribution-matching objective. We provide a gradient analysis that motivates this objective choice under ideal tracking. Building on this, SGMD introduces a pair of dual potentials: negative-residual (NR) for outer-loop correction and residual-contraction (RC) for inner-loop tracking. Empirically, compared to DMD2, SGMD achieves an approximately $\sim 3\times$ training speedup and substantially improves motion dynamics for 4-step distilled models while preserving temporal consistency. A human study confirms that SGMD is preferred in motion quality and overall preference, while visual quality and text alignment remain comparable. Code is available at https://github.com/ModelTC/LightX2V.

Recent video diffusion foundation models have achieved remarkable progress in high-quality video generation, yet turning them into real-time interactive video world models remains challenging. Interactive world models require controllable, causal, and low-latency rollout, which in practice demands a full pipeline spanning data construction, controllable fine-tuning, autoregressive training, few-step distillation, and streaming inference. In this work, we present minWM, a full-stack open-source framework for building real-time interactive video world models. minWM provides an end-to-end pipeline that converts existing bidirectional T2V/TI2V video foundation models into camera-controllable few-step autoregressive world models. Specifically, minWM first fine-tunes a bidirectional video diffusion model with camera control, and then applies the Causal Forcing / Causal Forcing++ pipeline, including AR diffusion training, causal ODE or causal consistency distillation, and asymmetric DMD, to distill it into a few-step autoregressive generator for low-latency rollout. The framework is modular and architecture-extensible: we instantiate it on representative open backbones, including Wan2.1-T2V-1.3B and HY1.5-TI2V-8B, covering both cross-attention-based condition injection and MMDiT-style architectures. minWM also supports adapting existing video world models, such as HY-WorldPlay, to new data distributions, training recipes, and latency targets. Beyond releasing runnable scripts, checkpoints, documentation, and inference code, we provide practical ablations on camera trajectory quality, controllability training steps, and minimal batch-size requirements. We hope minWM serves as a reproducible and extensible recipe for building and adapting real-time interactive video world models. Project Page: [https://github.com/shengshu-ai/minWM](https://github.com/shengshu-ai/minWM)

Diffusion Large Language Models (dLLMs) have emerged as a promising non-autoregressive generative paradigm. Given the prohibitive computational cost of full fine-tuning, Parameter-Efficient Fine-Tuning (PEFT) has become the standard approach. However, existing PEFT methods (e.g., LoRA), originally tailored for autoregressive models, rely on static parameters that are agnostic to the noise level. Consequently, they ignore the intrinsic dynamics of the diffusion process, where input distributions and generation difficulty shift significantly along the denoising trajectory, rendering them suboptimal for dLLMs. To address this, we propose Noise-aware Low-Rank Adaptation (NaRA), which introduces a low-rank core matrix generated by a lightweight, globally shared hypernetwork conditioned on the noise level. This design enables the update matrices to vary continuously along the diffusion process while keeping parameter and latency overhead negligible. We provide a theoretical justification for the proposed NaRA framework and empirically demonstrate consistent improvements over noise-agnostic baselines across commonsense reasoning, mathematical reasoning, and code generation benchmarks. Our code is available at https://github.com/generaldi/NaRA.

Scaling Diffusion Transformers to generate high-resolution, long videos is constrained by the quadratic cost of self-attention, and existing sparse attention methods degrade under high sparsity. We show empirically that generation quality is determined not by the sparsity ratio itself, but by how well the sparse mask aligns with the tile-wise geometry of full attention. Based on this insight, we propose Veda, a distilled sparse attention framework that formulates tile selection as an explicit reconstruction problem from full attention. Veda integrates statistics-aware tile scoring with head-aware tiling to reduce estimation error and structural mismatch, enabling aggressive sparsity. A hardware-efficient tile-skipping kernel converts theoretical sparsity into practical wall-clock speedups. Experiments on large video diffusion models, including Waver and Wan2.1, demonstrate substantial acceleration with no noticeable degradation in generation quality. To generate 720P 10-second videos on Waver-T2V-12B, Veda achieves a 5.1$\times$ end-to-end speedup and a 10.5$\times$ self-attention speedup, reducing attention overhead from 92% to 50%. Notably, the gains increase with sequence length, indicating that Veda scales favorably with spatiotemporal resolution across models.

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most $\widetilde{O}(\varepsilon^{-k \vee 2})$ samples to achieve $\varepsilon$ error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

We investigate conditional diffusion modeling for three-dimensional 21 cm lightcone emulation, focusing on cubes with a sky-plane size of $64\times64$ and a line-of-sight depth up to 1024 cells. Relative to earlier 2D studies, the 3D setting is substantially harder because memory limits enforce very small micro-batches while the underlying voxel distribution is highly skewed and long tailed. We perform controlled comparisons across preprocessing choices, dynamic-range compression settings, architecture depth, and training duration using $25{,}600$ training lightcones and validation ensembles at fixed parameter points. For validation, each reference parameter point contains 800 21cmFAST realizations with independent initial conditions, and we use 800 samples per model and per reference set for the reported ensemble comparisons. We evaluate generated lightcones with complementary diagnostics in both image and summary-statistic spaces: brightness-temperature slices, the global signal, the power spectrum, and reduced scattering coefficients. Across the tested configurations, preprocessing is the dominant factor governing stable training and the resulting physical fidelity. Among the configurations explored here, Yeo-Johnson preprocessing combined with moderate amplitude compression gives the most consistently favorable trade-off, with the strongest quantitative support coming from rankings based on the standard-deviation-normalized mean absolute error ($\mathrm{MAE}_{\rm std}$) of the global signal and qualitatively compatible behavior in the complementary diagnostics. At the same time, visually plausible 3D samples still retain measurable biases in two-point and higher-order statistics. We therefore view the present work as a simulation-level baseline for three-dimensional 21 cm emulation and for future studies that incorporate more realistic observational effects.

Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative models remains poorly understood: after a task change, what aspects of the learned distribution are most easily lost, and what replay samples should be prioritized? We address these questions through the modern Hopfield energy. Recent links between modern Hopfield networks (MHNs) and diffusion models allow analyses in MHNs to be transferred to diffusion models. We introduce intrinsic forgetting as an increase in Hopfield energy after the task change. In tractable settings in an MHN, we prove that high-energy, outlier-like samples undergo a larger energy increase than cluster-like samples, implying that samples located in sharp, isolated basins are more forgettable. We further analyze memory replay and show that replay is particularly effective for high-energy samples, enabling an energy-based selection of replay samples. We validate these predictions in experiments on MHNs and two diffusion models under continual-learning settings: Stable Diffusion and a pixel-space DDPM. In these diffusion models, Hopfield energy tracks reconstruction-based forgetting, and replay experiments reveal energy-dependent mitigation of forgetting that is consistent with the MHN analysis.

We study real-time audio-responsive character control as a deployment-faithful problem: strictly causal, bounded-latency streaming that must generate coherent full-body motion at interactive frame rates while the audio condition can change abruptly, including tempo shifts, drops, or user edits. Prior music-to-motion systems are largely optimized for offline generation with global context, and degrade in streaming rollouts where conditioning history becomes stale or unreliable. We introduce DiscoForcing, a streaming audio-driven diffusion framework that combines a causal music encoder that captures rhythmic structure and phase dynamics with a diffusion-forcing sequence model trained under heterogeneous noise levels across the temporal horizon. Building on this, we design a hybrid temporal schedule and a history-guided streaming sampler to explicitly trade off responsiveness against long-horizon consistency under non-stationary audio. Implemented in an end-to-end real-time interactive system with online avatar playback and humanoid deployment workflows, DiscoForcing delivers more stable long-horizon rollouts and sharper audio-motion alignment than prior baselines under matched causality and latency constraints while maintaining real-time throughput.

Predicting how a cell will change its transcriptional state under a developmental signal or a genetic perturbation is the computational core of in-silico biology and the AI Virtual Cell program. Existing approaches either fit static control-to-treated maps that discard time, or solve multi-step ODE / Schrödinger-bridge problems on each dataset independently. We introduce Chreode, a one-step cell world model that predicts action-conditioned cell-state transitions through a structured residual transition operator. It shifts distributional evolution from inference time to training time, enabling single-pass generation while preserving a Waddington-inspired decomposition into downhill landscape flow, rotational in-tangent dynamics, and stochastic spread. The model is pretrained with a shared scVI encoder and a DiT-based dynamics backbone on a 2.4M-cell mouse embryonic atlas spanning 7 datasets. As a fine-tuning initialization, Chreode improves per-target Sinkhorn distance on Weinreb hematopoiesis and Veres islet differentiation over matched scratch models, PI-SDE, and PRESCIENT. As a transferable gene-state embedding for GEARS, the pretrained dynamics representation reduces shared-vocabulary DE20 mean squared error on Norman Perturb-seq from 0.2121 to 0.1858, a 12.4% relative improvement, without changing the GEARS training procedure. We interpret this transfer to perturbation prediction as evidence that pretrained developmental-trajectory dynamics encode differentiation primitives transferable to CRISPR-induced state shifts, since both involve cell-state transitions in a shared latent geometry. The pretrained backbone additionally produces zero-shot clonal fate scores on Weinreb that are competitive with strong dynamic-OT baselines.

The distortion-perception (D-P) tradeoff is a fundamental phenomenon of Bayesian inverse problems, which characterizes the inherent tension between distortion performance and perceptual quality. Enabling flexible traversal of the D-P tradeoff at inference time is crucial for practical applications. Despite the recent success of diffusion models in zero-shot inverse problem solving, efficient and principled strategies for D-P traversal in diffusion-based inverse algorithms remain inadequately characterized. In this paper, we propose a stage-wise framework for realizing D-P traversal using a single diffusion model in zero-shot inverse problems. Our proposed method, termed MAP-RPS, starts with an MAP estimation stage that approximates the MMSE solution and provides a low-distortion initialization, followed by a re-noised posterior sampling stage that progressively improves perceptual quality. We provide theoretical analyses for both stages, establishing the validity and effectiveness of the proposed design. Furthermore, we extend MAP-RPS to the latent space, yielding LMAP-RPS, which enjoys broader applicability by leveraging large-scale pre-trained latent diffusion backbones. Extensive experiments demonstrate that MAP-RPS and LMAP-RPS enable more effective D-P traversal on various tasks, while also exhibiting strong performance as efficient solvers for real-world inverse problems.

Product images strongly influence consumer decision-making in online marketplaces. Empowered by multimodal contrastive learning, generative AI can output images that closely align with text prompts. Yet existing generative AI models do not directly optimize marketplace performance. This is a critical gap, since semantic alignment alone does not guarantee that an image will sell. To address this limitation, we propose a utility-aware multimodal contrastive learning framework that incorporates consumer demand into a novel Utility-Aware InfoNCE loss. Optimizing this utility-aware objective guides generation toward images that are both semantically coherent and demand-enhancing. This effect arises directly from a shift in the learned image-text representation space toward demand-driven visual cues, which we also validate through the theoretical bound of the proposed objective. In downstream applications on Amazon and Airbnb, product images generated and edited by our method outperform state-of-the-art models in increasing demand and preserving fidelity, while maintaining text-image consistency. Notably, our utility-aware framework preserves inverse U-shaped demand patterns for attributes such as aesthetics and uniqueness, improving demand-based performance while preserving fidelity and semantic consistency. Human-subject experiments further validate its commercial effectiveness. As generative AI technology continues to evolve, our utility-aware component can be flexibly embedded into emerging generative models to improve direct commercial use.

We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, but, especially for uniform-rate models, they often require many steps to generate a single sample. Existing acceleration methods either rely on training additional quantities or suffer from slow mixing. In this work, we propose a novel Gibbs-based corrector for discrete diffusion models, termed Gibbs-Accelerated Discrete Diffusion (GADD). GADD leverages the structure of the concrete score function to construct Gibbs posterior likelihoods directly, without requiring any additional training beyond standard score estimation. We show that GADD achieves an overall sampling complexity of $\mathcal{O}(\mathrm{polylog} (\varepsilon^{-1}))$, yielding the first such rate for diffusion-based samplers for uniform-rate discrete diffusion models. We also conduct numerical experiments demonstrating the practical advantages of GADD across synthetic data, zero-shot text sampling, and zero-shot conditional music generation. These results corroborate the theory and show that GADD consistently improves sample quality and wall-clock efficiency over standard baselines, including vanilla Euler methods and CTMC correctors. Beyond this, our theoretical analysis introduces a novel framework for analyzing predictor-corrector methods in discrete diffusion models, which may be of independent interest. Unlike existing approaches that rely on the Girsanov change-of-measure technique, our method is based on an induction argument that tracks error propagation across predictor iterations while accounting for inaccuracies in the corrector updates.

Unsupervised visual object tracking is a challenging task that requires following arbitrary targets in videos without training on ground-truth annotations. Despite considerable progress, existing state-of-the-art unsupervised trackers often struggle in scenarios that demand fine-grained understanding of semantic and visual structural information within video frames. Text-to-image diffusion models are well known for their ability to generate images that accurately reflect the semantics and structures described in the input prompt, demonstrating a strong grasp of visual semantics and structures. Building on this capability, we approach the unsupervised tracking from a new perspective by exploiting the rich semantic knowledge encoded in pretrained text-to-image diffusion models. To adapt the diffusion models, which are originally developed for image generation, to the tracking task, we reinterpret the models as a bridge between text and image modalities. This connection is realized through the cross-attention mechanism: when both text and an image are input into the models, they highlight the regions of the image that are semantically aligned with the text in the cross-attention maps. We therefore learn a prompt that represents the tracking target and activates its corresponding region in the cross-attention map for each frame, which enables object tracking with the diffusion model. Specifically, our method Diff-Tracking is composed of two main components: an initial prompt learner and an online prompt updater. The initial prompt learner generates a prompt that captures the target object in the first frame, allowing the diffusion model to identify the target. The online prompt updater refines the prompt based on motion information, enabling consistent tracking across video frames. We evaluate our approach on six challenging tracking datasets demonstrate the effectiveness of our approach.

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.