Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential. Indeed, for specific constraint satisfaction tasks (e.g., sudoku puzzles), this capability has proven to be highly advantageous. However, in this paper, we reveal that for general reasoning tasks (e.g., mathematics and coding), arbitrary order generation may in fact limit the reasoning potential of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of solution coverage. This observation motivates a rethink of RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning can be better elicited by simply forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, **JustGRPO**, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs.
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Deep Learning · Large Language Models
Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential. Indeed, for specific constraint satisfaction tasks (e.g., sudoku puzzles), this capability has proven to be highly advantageous. However, in this paper, we reveal that for general reasoning tasks (e.g., mathematics and coding), arbitrary order generation may in fact limit the reasoning potential of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of solution coverage. This observation motivates a rethink of RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning can be better elicited by simply forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, **JustGRPO**, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs.
Probabilistic Methods · Monte Carlo and Sampling Methods
Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD-Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models. However, it remains unclear how to tune the algorithm's hyperparameters in a principled manner to ensure the uncertainty estimates are statistically meaningful. In this work, we address this gap in tuning guidance by developing a statistical scaling limit theory for SGLD-Gibbs. We derive a joint asymptotic limit for the global parameters and latent variables under appropriate space-time rescaling. We show that global parameters converge to a diffusion-type limit, while individual latent variables converge to a jump process reflecting their intermittent Gibbs updates. This joint jump-diffusion structure reveals how latent-variable randomness contributes to the stationary distribution of the global parameters. We leverage our results to provide explicit guidance on hyperparameter tuning for SGLD-Gibbs that ensures meaningful uncertainty quantification. Our empirical results show that SGLD-Gibbs with our tuning guidance leads to better parameter estimates and uncertainty quantification than stochastic variational inference.
Video subtitle removal is essential for content localization and media re-editing, yet existing mask-guided diffusion methods face critical limitations: training inefficiency requiring extensive annotations and full model fine-tuning, inference complexity demanding explicit mask sequences, and static prior utilization unable to adapt to quality variations. We present CLEAR (Context-aware Learning for End-to-end Adaptive subtitle Removal), a lightweight adapter-based framework addressing these challenges through three technical innovations. First, self-supervised prior learning (Stage I) extracts occlusion guidance from video pairs using pixel differences as weak supervision, eliminating annotation dependency while learning generalizable subtitle features across languages. Second, LoRA-based adaptive refinement (Stage II) enables parameter-efficient training that preserves pre-trained visual priors while achieving true mask-free end-to-end inference without external detection modules. Third, adaptive focal weighting dynamically adjusts prior influence based on local quality assessment, effectively handling diverse subtitle styles and noisy guidance signals. Extensive experiments demonstrate CLEAR's superior performance in multilingual subtitle removal while requiring only 0.77% trainable parameters, establishing a new paradigm for efficient video text removal without inference-time mask dependencies.
Theory · Domain Adaptation and Transfer Learning
Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $\tilde{\mathcal{O}}(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tilde{\Omega}(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.
Applications · Computer Vision
Group Relative Policy Optimization has emerged as essential for aligning video diffusion models with human preferences, but faces a critical computational bottleneck: training a 14B parametered model typically demands hundreds of GPU days per experiment. Existing efficiency methods reduce costs through sliding window subsampling training timesteps, but fundamentally compromise optimization, exhibiting severe instability and failing to reach full trajectory performance. We present Flash-GRPO, a single-step training framework that outperforms full trajectory training in alignment quality under low computational budgets while substantially improving training efficiency. Flash-GRPO addresses two critical challenges: iso-temporal grouping eliminates timestep-confounded variance by enforcing prompt-wise temporal consistency, decoupling policy performance from timestep difficulty; temporal gradient rectification neutralizes the time-dependent scaling factor that causes vastly inconsistent gradient magnitudes across timesteps. Experiments on 1.3B to 14B parameter models validate Flash-GRPO's effectiveness, demonstrating substantial training acceleration with consistent stability and state-of-the-art alignment quality.
Applications · Health / Medicine
Predicting spatial gene expression from routine H\&E makes high-resolution molecular profiling accessible at scale, especially for large retrospective cohorts. However, current models mostly treat gene expression as a series of pointwise tasks. While effective for numerical fitting, this approach overlooks biological structures: the functional coordination between genes and their organized distribution across tissue. We reframe this task as structured distribution modeling and introduce \textbf{FLAG}, a diffusion-based framework designed to preserve these biological relationships. To capture such structures, a natural strategy would be to jointly model gene expression and their spatial interactions. However, we identify a critical \textbf{Gene Dimension Curse}: such joint modeling fails in high-dimensional gene spaces. This motivates FLAG, which conditions the generative process using a novel spatial graph encoder to ensure gene-spatial topographic coherence and a Gene Foundation Model (GFM) alignment to maintain high gene-gene structural fidelity. To rigorously assess our approach, we propose a structural evaluation metrics, including Gene Structural Correlation (\textbf{GSC}) and Spatial Structural Correlation (\textbf{SSC}). Our experiments demonstrate that FLAG is highly competitive with or superior to state-of-the-art models in traditional accuracy (PCC/MSE), while achieving significantly enhanced structural fidelity in capturing both gene-gene and gene-spatial relationships.
Theory · Deep Learning
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, the equivalence, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion generation are estimated by maximizing the quasi-likelihood, ensuring a consistent matching of both the first two transition moments between every two time points. A stochastic sampler is introduced to facilitate the computation that leverages both the estimated score and Hessian information. We establish consistency of the quasi-maximum likelihood estimation, and provide non-asymptotic convergence guarantees for the proposed sampler, quantifying the rates of the approximation errors due to score and Hessian estimation, dimensionality, and the number of diffusion steps. Empirical and simulation evaluations demonstrate the effectiveness of the proposed Likelihood Matching and validate the theoretical results.
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed form, and its resolution via discretization typically requires many small iterations to produce \emph{high-quality} samples. More precisely, prior works have shown that the iteration complexity of discretization methods for diffusion models scales polynomially in the ambient dimension and the inverse accuracy $1/\varepsilon$. In this work, we propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method, and we prove that its iteration complexity scales *polylogarithmically* in $1/\varepsilon$, yielding the first "high-accuracy" guarantee for a diffusion-based sampler that only uses (approximate) access to the scores of the data distribution. In addition, our bound does not depend explicitly on the ambient dimension; more precisely, the dimension affects the complexity of our solver only through the *effective radius* of the support of the target distribution.
Applications · Computer Vision
The rapid evolution of generative AI, from GANs to modern diffusion models, has resulted in increasingly subtle discriminative clues. These fine-grained signals are often overshadowed by dominant, high-fidelity image content (e.g., the main subject), limiting the reliability of existing detectors that predominantly rely on global representations. To address this challenge, we propose the Peak-Guided Calibration (PGC) framework. PGC introduces a novel strategy that aggregates salient features via a peak-focusing mechanism. Specifically, by employing a peak-sensitive aggregation that accentuates the most discriminative local clues, PGC leverages these critical signals to calibrate the global decision. This approach recovers subtle patterns that would otherwise be submerged in the global context. Furthermore, to better simulate real-world threats, we introduce the CommGen15 dataset, a challenging benchmark comprising samples from 15 commercial models. Extensive experiments demonstrate that PGC achieves state-of-the-art performance, surpassing existing detectors by +12.3% (Accuracy) on CommGen15, while setting new records on standard benchmarks, including GenImage (+2.1%), AIGI (+3.5%), and UniversalFakeDetect (+1.7%).
Applications · Computer Vision
Recovering 3D human poses for multiple individuals from different camera views is a fundamental bottleneck for analyzing interacting behaviors. Existing self-supervised approaches leverage synthetic catalogues of 3D poses; however, this leads to poor generalization in real-world scenarios due to distribution shifts. We therefore introduce DisPOSE, a self-supervised framework that approximates the inherently discrete multi-view person-assignment problem as a generative diffusion process over the space of polystochastic tensors. By employing differentiable Sinkhorn projections during denoising, our model learns to guide solutions toward valid and feasible assignments based on 2D image priors. The complete 3D skeletons of localized individuals are then regressed using a Hypergraph-Convolutional Decoder that explicitly models relational structures and articulated joints across multiple views. The proposed approach outperforms current state-of-the-art self-supervised methods on standard datasets and demonstrates strong performance on a newly proposed benchmark featuring highly occluded scenes from surgical operating rooms. Our diffusion-based localization demonstrates high label efficiency, retaining 99\% of its performance with only 10\% of the pseudo-labels. Notably, disentangling the assignment and root regression components while maintaining differentiability makes DisPOSE nearly agnostic to different camera arrangements.
Deep Learning · Graph Neural Networks
Higher-order structures are powerful relational modeling tools, yet existing spectral operators decompose topology into separate ranks, leaving practitioners to fuse information back to vertices through ad-hoc choices. We introduce _Collapsed Effective Operators_, which marginalize higher-order structures into a single vertex-level operator via Schur complementation of a graded Laplacian. This yields a dense operator that encodes long-range interactions mediated by topology and is applicable to arbitrary higher-order constructs. We show it preserves positive semi-definiteness with a strict spectral upper bound relative to the rank-0 Laplacian, effectively lowering system energy under higher-order connectivity. Empirically, our operator significantly improves spectral clustering, enables diffusion over topological structures, and accelerates the processing of higher-order structures with neural networks.
Deep Learning · Generative Models and Autoencoders
One emerging approach to mitigating data heterogeneity in Federated Learning (FL) is to employ diffusion models to generate synthetic data for clients, thereby aligning local data distributions with the global distribution. Prior work has primarily focused on balance-oriented augmentation, which assumes a balanced global class distribution and thus generates samples of rare classes to rebalance each client's local dataset. However, in practice, global data distributions are often inherently imbalanced. Moreover, privacy constraints in FL hinder the server’s ability to accurately estimate the global distribution, rendering balance-oriented augmentation suboptimal. This raises a key, underexplored challenge: How can synthetic data be generated and selected to align local distributions with the true, yet unknown, global distribution? Our key insight is that a model’s performance implicitly reflects the data distribution it has been trained on. Based on this observation, we use the performance discrepancy between local and global models to identify the regions where each client’s local dataset is lacking, and generate corresponding samples for clients. Furthermore, we adapt the diffusion model via preference optimization, enabling it to generate data that better aligns with the true global distribution. Extensive experiments on multiple benchmarks demonstrate that FedPDG outperforms state-of-the-art methods, achieving up to 3.82\% improvement.
General Machine Learning · Data
Generative tabular augmentation is appealing in data-scarce domains, yet the prevailing focus on distributional fidelity does not reliably translate into better downstream models. We formalize a *fidelity-utility gap*: common generative objectives prioritize distributional plausibility, whereas augmentation succeeds only when injected samples reduce the current learner's held-out evaluation loss. This gap motivates learning not just how to generate, but what to generate and when to inject as training evolves. We propose TAP (Tabular Augmentation Policy), which couples diffusion inpainting with a lightweight, learner-conditioned policy to steer generation toward high-utility regions and controls safe injection via explicit gating and conservative windowed commitment. Under severe data scarcity, TAP consistently outperforms strong generative baselines on seven real-world datasets, improving classification accuracy by up to 15.6 percentage points and reducing regression RMSE by up to 32%.
Deep Learning · Generative Models and Autoencoders
We present Causal-Adapter, a modular framework that adapts frozen text-to-image diffusion backbones for counterfactual image generation. Our method enables causal interventions on target attributes while preserving all other aspects of the image, including the core identity. In contrast to prior approaches that rely on prompt engineering without explicit causal structure, Causal-Adapter leverages structural causal modeling augmented with two attribute regularization strategies: prompt-aligned injection, which aligns causal attributes with textual embeddings for precise semantic control, and a conditioned token contrastive loss to disentangle attribute factors and reduce spurious correlations. Causal-Adapter achieves state-of-the-art results on synthetic and real-world datasets, outperforming other baselines in effectiveness, composition, realism, and minimality. These results demonstrate that the approach enables efficient, robust, and generalizable counterfactual image editing with faithful attribute modification and strong preservation of core identity.
Deep Learning · Attention Mechanisms
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. Empirically, 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 directly modifying the circulation of the underlying dynamics.
Modeling complex dynamics from observational data is fundamental to scientific discovery and artificial intelligence. However, existing approaches ranging from Neural ODEs to diffusion models are often plagued by the entanglement of static state representations and instantaneous motion, leading to accumulated errors and off-manifold hallucinations where predicted trajectories violate intrinsic geometric constraints. To address this, we propose Geometric Flow Grounding, a unified framework that enforces dynamic evolution strictly along the tangent bundle of the learned data manifold via a differentiable Neural Tangent Projection Layer. By geometrically decoupling state representation from tangential dynamics, our method generalizes across diverse data regimes. In the context of scientific discovery, we demonstrate that the projection layer eliminates numerical aliasing in sparse dynamical systems and recovers interpretable gene regulatory motifs from single-cell data by disentangling states from developmental velocities. Bridging to trustworthy AI, we further repurpose the geometric projection residual as a zero-shot metric for deepfake video detection, identifying generative inconsistencies against the implicit flow of pre-trained world models. Our results establish manifold-constrained projection as a universal operator for both discovering natural laws and verifying synthetic content.
We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d\mathrm{polylog}(1/\delta))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\mathrm{polylog}(1/\delta))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\mathrm{polylog}(1/\delta))$. Our approach also yields the first $\mathrm{polylog}(1/\delta)$ complexity sampler for general log-concave distributions using only gradient evaluations.
Deep Learning · Large Language Models
Diffusion-based language models (dLLMs) enable parallel token generation through iterative denoising, but existing decoding strategies collapse to single-token generation under low confidence, severely limiting throughput. Unlike autoregressive models where speculative decoding operates on token sequences in a fixed left-to-right order, dLLMs require speculating over \emph{denoising trajectories}—sequences of multi-token updates with explicit positions and unmasking orders. We develop a trajectory-level speculative framework that constructs draft denoising trajectories via confidence-stratified tree exploration and verifies them through blockwise parallel evaluation with bidirectional attention masking. Our method further introduces inter-block speculation, exploiting diffusion models' bidirectional structure to perform cross-block lookahead. We formally characterize when this approach is exact and identify trajectory drift as the fundamental cost of increased parallelism. Building on Fast-dLLM's dual-cache infrastructure, our framework reduces denoising iterations by 30-40\% and increases tokens-per-step from 2.6 to 4.3, achieving 7-14$\times$ speedup over vanilla dLLMs and 1.3$\times$ over Fast-dLLM with less than 1\% accuracy change across reasoning and code benchmarks.
Applications · Robotics
Evaluating generalist robot manipulation policies is costly and difficult to scale in the real world. While emerging world models (e.g., WorldEval, Ctrl-World) offer a promising alternative, the reliability of such evaluation remains a critical bottleneck. Specifically, their visual predictions can undermine policy assessment by "self-correcting" failures into false positives or yielding artifacts under out-of-distribution controls. Even with failure-enriched data, current architectures struggle to capture action-causal dynamics, as they typically treat actions as passive conditions rather than causal drivers. To address this, we propose dWorldEval, an action-centric discrete-diffusion world model that maps visual observations, language instructions, and action chunks into a shared unified token space and denoises them with a single self-attention backbone where actions function as first-class tokens. To realize reliable policy-world interaction, dWorldEval introduces a sparse keyframe memory that anchors global scene state while preserving fine-grained multi-view interaction cues, and leverages Progress-as-text to jointly generate future observations and success indicators. Extensive experiments on LIBERO, RoboTwin, and real-robot tasks demonstrate that dWorldEval significantly outperforms video diffusion baselines in action controllability, stabilizes long-horizon multi-view rollouts, enabling accurate policy ranking via automatic success estimation.