生成模型理论与方法

Diffusion models generate skillful weather ensembles but require costly iterative sampling. We introduce a supervised energy-distance distillation method that compresses a multi-step diffusion teacher into a single-step student by aligning student forecasts with teacher samples and ground-truth observations. Experiments on global forecasting and typhoon-track prediction show that our student outperforms existing distillation methods and preserves skill for extreme events. It matches or surpasses the teacher across key metrics using only one neural function evaluation per autoregressive step.

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 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 7-14x speedup over vanilla dLLMs and 1.3x over Fast-dLLM with less than 1% accuracy change across reasoning and code benchmarks.

This paper proposes a novel data-driven algorithm to approximate the dominant eigenfunctions (aka.~modes) of the Koopman operator of nonlinear dynamical systems using neural networks. The relevance of learning the dominant Koopman modes is to approximate nonlinear dynamics by linear ones in a lifted space, thereby enabling simplified control and analysis. To fight the curse of dimensionality arising from using expressive templates (here neural networks) for the mode approximation, the proposed method leverages a power-iteration scheme that directly learns the dominant Koopman modes without explicitly constructing the projection of the Koopman operator on the template of functions. Our approach connects to other approaches in the literature that avoid the curse of dimensionality by learning small dictionaries of functions, but differs from them in that we do not require ``anti-collapse mechanisms'' to ensure that the learned dictionary is expressive enough to approximate the Koopman operator since our power-iteration scheme is designed to converge toward the dominant modes of the projected Koopman operator. The approach is fully data-driven, requiring only sampled state transitions. Theoretical guarantees are provided, showing convergence under increasing sample size and network width (in connection with the neural tangent kernel theorem). Numerical experiments demonstrate that the method achieves accurate and smooth approximations of dominant modes while avoiding the limitations of traditional techniques such as extended dynamic mode decomposition.

Decentralized learning systems aim to collaboratively train models across multiple clients without relying on a central coordinator. While decentralization improves scalability, privacy, and robustness, it also exacerbates three fundamental challenges: statistical heterogeneity across clients, fairness in client-level performance, and stringent communication constraints. This raises a natural question: how fair can decentralized learning be under limited communication? We address this question by presenting a unified framework for decentralized learning under communication constraints, bringing together graph-based personalization, agnostic fairness, and compressed event-triggered communication. Specifically, we propose a new algorithm DMFL-SQ, a decentralized multi-task learning algorithm that couples personalized model training over a communication graph with an agnostic mixture fairness objective, while reducing communication through sparsification, quantization, and event-triggered synchronization. We establish convergence guarantees for general non-convex objectives and show that DMFL-SQ achieves an $\mathcal{O}(T^{-1/2})$ rate in expected squared Moreau-envelope stationarity despite sparse, quantized, and event-triggered communication. We further derive PAC-Bayes generalization guarantees for the fairness-aware mixture objective. Experiments on CIFAR-10 and the real heterogeneous MUSMET EEG dataset demonstrate that DMFL-SQ substantially reduces communication while maintaining predictive performance and improving fairness across clients. Together, our theoretical and empirical results show that personalization, fairness, and communication efficiency can be jointly achieved in decentralized learning while preserving the dominant convergence rate.

Peer effects are difficult to estimate when interaction graphs evolve because pre-assignment network history, dynamic peer exposure, and post-assignment network change have distinct causal roles. We introduce a controlled contrast framework that indexes potential outcomes by own treatment, temporally aggregated peer exposure, and a post-assignment evolution summary. Differences between the resulting means define own-treatment, peer-exposure, controlled network-evolution, and joint controlled contrasts rather than a mediation decomposition. We develop the Dynamic Network Doubly Robust estimator, DynaNet-DR, which combines a temporally factorized propensity with normalized augmentation. Under consistency, summary sufficiency, sequential exchangeability, positivity, nuisance convergence, and weak dependence, its canonical estimator is consistent when either the outcome regression or the propensity estimator is consistent. The reported implementation adds representative-score prediction, fixed clipping, and finite-sample stabilization. Semi-synthetic benchmarks on fixed real temporal graph sequences show favorable estimation accuracy among methods targeting the full profile. These benchmarks assess summary-indexed contrasts rather than counterfactual edge generation, and the MathOverflow study is an observational illustration under the stated assumptions.

Discrete diffusion models have become a strong, widely adopted class of generators for sequence data, and steering them toward a downstream reward at inference time, without any retraining, is increasingly important. Such training-free steering is done by gradient guidance, by search, or by combining the two. We study the combined regime and identify two weaknesses in how it is usually run: the guided proposal estimates its gradient from a single noisy sample, and the search then resamples particles at a fixed temperature that ignores how rewards spread across each denoising step. We address both with a small set of changes that add no denoiser cost. For the proposal, we lower the estimator variance with a Rao-Blackwellized reveal for differentiable rewards and a leave-one-out baseline for non-differentiable ones; for the search, we standardize the per-step values into a group-relative advantage and prove it collapses to a single active ingredient, an adaptive resampling temperature. We call the resulting method Guided Reduced-variance proposals and Adaptive Selection (GRAS). GRAS is simple yet effective: across regulatory DNA and protein design it attains the best training-free reward, outperforming prior training-free methods and matching or surpassing a reward-fine-tuned model, and it remains effective even for non-differentiable rewards.

Specializing large language models to vertical domains improves domain-specific behavior but often degrades general capabilities such as reasoning, coding, instruction following, and creative writing. We study this domain--general trade-off in Multi-Teacher On-Policy Distillation (MOPD), where a specialized student is supervised on its own sampled trajectories by domain and general teachers. Standard MOPD faces two limitations: ordinary on-policy sampling rarely exposes tokens with large positive teacher--student advantages, while the advantage sign alone does not establish whether the resulting update direction is reliable. We propose uncertainty-calibrated MOPD to address these limitations. Dual-temperature sampling broadens the candidate trajectory pool, and positive-advantage-density filtering selects trajectories with stronger positive learning signals. Centered log-likelihood (CLL) filtering then computes an entropy-calibrated teacher-endorsement score and probabilistically retains token updates according to direction--endorsement consistency. Experiments on role-playing and medical-domain specialization show that our method improves the general-capability average over standard MOPD by $4.73%$ and $10.84%$, respectively, while maintaining vertical-domain performance. Ablations and diagnostic analyses further confirm that the gains do not merely result from a larger rollout budget and that the proposed trajectory- and token-level mechanisms address their intended failure modes.

Molecular crystal structure prediction (CSP) is important in pharmaceuticals, agrochemicals, and organic electronics, where subtle differences in molecular conformation and packing can strongly affect material properties. We present Packora, a flow-based generative model for molecular CSP that jointly predicts atomic coordinates and the lattice from molecular graphs. Packora supports multi-component and organometallic crystals and can condition on any subset of molecular conformers, stereochemical labels, and space-group information within a single model. Inspired by the CCDC CSP blind test, we evaluate generation and ranking separately, using generation to isolate generator quality and ranking to measure end-to-end performance under a common relaxation and ranking pipeline. We also systematically study architecture, training, conditioning, inference, and scaling, identifying an effective design based on cacheable pairwise reasoning, training objective and numerical solver choices, conditioning dropout, and balanced scaling of pairwise and single representations. Packora outperforms the baselines on both structure generation and ranking benchmarks, achieving the best matched-budget coverage across all six generation benchmarks, as well as higher experimental-form recovery, lower experimental-form ranks, and faster convergence in ranking.

Diffusion models can be used to generate spatiotemporal signals of physical phenomena, such as time-series images of fluid dynamics. However, a major limitation of standard diffusion models is that they do not incorporate constraints derived from the underlying physical laws. Consequently, generated samples may appear visually plausible while deviating substantially from the true dynamics. In this study, we propose a simple yet effective physics-informed approach based on diffusion guidance with self-generated data augmentation. The proposed method learns the data distribution conditioned on the degree of deviation from the physically correct dynamics and generates samples by explicitly setting the deviation condition to be zero. The method decouples the evaluation of the governing equations from the diffusion model training and sampling processes, avoiding the need to solve the governing equations at every iteration of the denoising process. This design makes the method applicable to problems requiring computationally expensive numerical simulations and enables faster sample generation. Experimental results demonstrate that the proposed model not only significantly reduces the deviations compared with standard diffusion models but also achieves further reductions when combined with existing physics-constrained diffusion methods.

Subseasonal-to-seasonal (S2S) precipitation forecasting has substantial financial and societal impact, yet remains challenging because of weak predictive signals, high associated uncertainty, and the computational cost of operational systems, which constrains simulation fidelity. We introduce SimCast-S2S, a generative latent-diffusion framework for probabilistic S2S precipitation forecasting that addresses three major bottlenecks in data-driven prediction. First, because S2S prediction requires uncertainty quantification rather than only deterministic point forecasts, SimCast-S2S is the first data-driven system that uses a diffusion-based generative pipeline for S2S prediction, enabling effective sampling from the underlying conditional distribution. Second, since generating large probabilistic ensembles is computationally costly in physical space, SimCast-S2S instead operates in a compact latent space learned by variational autoencoders (VAEs), enabling efficient large-ensemble generation. Third, diffusion models typically require large training datasets; SimCast-S2S overcomes this via transfer learning with low-rank adaptation (LoRA), pretraining on large ensembles of climate simulations before fine-tuning on limited reanalysis data. On reanalysis data, SimCast-S2S outperforms deep learning baselines, including convolutional neural networks and U-Net architectures. Notably, despite using only a subset of atmospheric input variables and no post-processing, bias correction, or calibration, SimCast-S2S remains competitive with, and in many aspects outperforms, state-of-the-art operational systems such as the ECMWF-S2S baseline. These results indicate that latent generative modeling combined with simulation-to-reanalysis transfer learning offers an efficient and scalable path toward data-driven probabilistic S2S precipitation forecasting.

Graphs are invariant under node permutations, motivating the use of permutation-equivariant architectures in generative models. In flow matching, however, symmetry may also enter the source--target coupling: once graph pairs are compared up to node relabeling, the natural Wasserstein geometry is that of the graph quotient space. The Euclidean quotient metric of this space coincides with the Gromov--Monge distance, obtained by optimally relabeling the nodes. We develop this perspective theoretically, showing that quotient couplings can be lifted to aligned representatives without additional cost and that symmetrization yields equivariant flow-matching minimizers, including for categorical endpoint prediction. In practice, exact Gromov--Monge alignment is intractable, so we construct minibatch couplings using efficient Gromov--Wasserstein-type relaxations and lower bounds for the inner node alignment, optionally combined with an outer assignment between graphs. The resulting procedure changes only the training coupling and is compatible with standard permutation-equivariant architectures. Across continuous graph and categorical molecular generation, these structure-aware couplings substantially improve sample quality at small integration budgets, while our scaled-up molecular models remain competitive under conventional many-step sampling.

On-policy distillation (OPD), which leverages a pre-trained, specialized teacher model to provide dense supervisory signals, has achieved significant success in Large Language Models (LLMs) and has recently been adapted to flow matching models. However, this paradigm suffers from two major issues: First, training a separate, task-specific teacher for every new objective incurs high computational costs. Second, the discrepancy between teacher and student distributions often leads to compounding errors along the generation trajectory. In this paper, we introduce Self-OPD, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision. At each timestep, Self-OPD branches the deterministic next-state prediction into $K$ stochastic SDE candidates, rolls them out with the ODE sampler, and compares their rewards against a deterministic self-reference baseline to obtain normalized advantages. The velocity field is optimized with an all-branch pull-push objective, where high-advantage branches attract the student and low-advantage branches repel it under direction-aware attenuation and SDE-variance normalization. For multi-objective alignment, Self-OPD fuses normalized scores at the reward level, avoiding direct gradient conflict. Experiments on single and mixed reward benchmarks show that Self-OPD outperforms prior RL and OPD methods without task-specific teachers.

Diffusion multimodal large language models (dMLLMs) have recently emerged as a new decoding paradigm for multimodal generation. Starting from a fully masked sequence, dMLLMs progressively decode the sequence by unmasking a subset of the remaining masked positions at each step. Since the selected tokens serve as the prediction context for subsequent steps, deciding which tokens to decode is crucial to the quality of the final output. The most common strategy prioritizes tokens based on a certainty measure that tends to favor tokens frequently observed in the training data. Recent approaches instead order tokens according to their influence on subsequent predictions, but do not explicitly account for the input image. We propose the Visual Information-Guided Sampler (VIG-Sampler), which prioritizes tokens based on their attention to image tokens. We further impose a constraint that penalizes candidate tokens whose image-attention distributions are similar to those of previously selected tokens, thereby increasing the information gain of the decoded subset. Extensive experiments on 7 captioning and VQA benchmarks with 3 open-source dMLLMs demonstrate the effectiveness of VIG-Sampler, which outperforms the Info-Gain Sampler by an average of 19.3 CIDEr points across the captioning benchmarks and surpasses it on COCO Caption while using only half as many decoding steps.

Muon has emerged as a strong optimizer for the matrix-valued parameters in large language model pretraining, approximately orthogonalizing its momentum with a few Newton-Schulz iterations. Existing theory either replaces this iteration with the exact polar factor it approximates, or treats its finite depth as an approximation error, and thus the iteration Muon actually runs can only hurt the guarantees. We show that finite Newton-Schulz can instead be beneficial for nonsmooth nonconvex optimization. To this end, we analyze Muon through the online-to-nonconvex conversion, which views the update rule as an online learner and converts its regret bound into a stationarity guarantee. The finite Newton-Schulz iteration smooths the discontinuous polar map into a Lipschitz map of the singular values, and Muon with finite Newton-Schulz can be regarded as an online learner with a smoothed spectral potential. This smoothing is exactly what the conversion needs: we prove that a Newton-Schulz depth growing only logarithmically in the target accuracy suffices for convergence to stationary points in nonsmooth nonconvex optimization, whereas Muon with the exact-polar update may fail to converge. The resulting sample complexity bounds match the best-known guarantees for nonsmooth nonconvex optimization and are optimal for smooth nonconvex optimization up to problem-dependent factors. The argument extends beyond Newton-Schulz to general spectral maps with the same smoothing property.

Open-ended Theory-of-Mind (ToM) trackers emit valid beliefs absent from finite references. A finite-reference-plus-matcher pipeline marks unmatched outputs false, creating proxy labels that can reverse proper-score model selection on fixed outputs. Holding 259 beliefs and paired scores fixed, reference recoding lowers weighted prevalence from 0.783 to 0.295 and reverses strictly proper Brier risk: a frozen source-prior rule leads native confidence by 0.227 under reference labels and trails by 0.152 under blinded adjudication, in all six authored scenarios. A reference-only Platt recalibrator reverses further. An ICE-specific reversal appears in a released 301-question NQ-open DPR-BERT pipeline: its average-confidence baseline improves instance-level calibration error by 0.045 under exact match but worsens it by 0.074 under human correctness, with both intervals excluding zero. On independently authored OpenToM narratives, 90-96% of audited unmatched beliefs are literally true and the paired direction again reverses. An exact decomposition attributes the distortion to omitted truths, and a closed-form criterion correctly classifies comparisons from twelve released systems. Frozen-audit retrospective replay shows 50 attempted annotations recover ranking direction with probability at least 0.996. TriSource-Restore anchors full-frame reference labels and frozen automatic judgments to a probability-sampled human pilot, maintains at least nominal coverage, narrows intervals, and repairs confidence subject to a base-rate deployment gate.

Co-speech gesture generation has made significant progress toward realistic full-body motion from speaker audio, yet existing models lack fine-grained spatial controllability of individual joints. To address this, we introduce InteractGesture, a model-agnostic, inference-time method for spatially controllable gesture generation. InteractGesture guides target latent estimates of a diffusion sampler through a differentiable RVQ-VAE decoder, backpropagating spatial control gradients to adjust motion latents during sampling. A primary challenge in streaming co-speech generation is chunk-wise dependency: standard sequential inference freezes prior chunks, preventing spatial constraints in future chunks from adjusting preceding trajectories and causing boundary inconsistencies. To overcome this limitation, we propose Progressive Chunk Guidance, a chunk-window strategy that maintains an active set of editable chunk latents with staggered delays, enabling spatial constraints to propagate gradients backward across chunk boundaries during streaming generation. Experiments on the BEAT2 dataset show that InteractGesture improves multi-joint spatial control while preserving overall gesture quality. Furthermore, our approach supports diverse applications, including sparse joint positioning, dense joint trajectory control, and directional pointing. Our project page is available at https://exitudio.github.io/interactgesture-page .

Dynamic contrast-enhanced breast MRI is central to cancer diagnosis and monitoring, but requires gadolinium-based contrast agents. In this work, we address pre-to-post contrast breast MRI synthesis for the MAMA-SYNTH challenge. We propose MAMA-FLUX.2, a conditional latent flow-matching approach based on FLUX.2-Klein-4B. The pre-contrast image is encoded as spatial conditioning, while the model predicts the flow field associated with the post-contrast target latent. To adapt the pretrained model efficiently, we use LoRA fine-tuning and introduce a regional training objective combining global flow matching, tumor-region supervision, and stable foreground regularization. We further investigate LoRA rank, intensity windowing, and regional loss weights on axial slices, prioritizing clinically relevant tumor-focused metrics. Our ablation study shows that moderate tumor and stable-foreground weighting improves the trade-off between image fidelity and tumor-region accuracy. The final model achieves the best overall balance with LoRA rank/$α=64/64$, $\mathrm{MHA}_{\max}=25$, $λ_{\mathrm{tumor}}=0.25$, and $λ_{\mathrm{stable}}=0.1$. These results demonstrate that compact pretrained rectified-flow transformers can be adapted for contrast-enhanced MRI synthesis using parameter-efficient fine-tuning and task-aware regional losses.

Forecasting a stochastic dynamical system rarely means a single number: one wants several observables---future state, threshold event, regime label---each with its own likelihood. Standard multi-task recipes balance per-task losses, tuned or learned. We instead compose the observables' likelihoods in per-task free-routed last-layer beliefs on a shared backbone; this absorbs unit-dependent loss scaling into likelihood parameters learned in the same gradient pass. Stochastic dynamics supply what static benchmarks cannot: computable ground truth for the predictive variance. Results land where theory puts them: on the well-specified, homoscedastic Ornstein--Uhlenbeck process the learned predictive law recovers the analytic kernel and correctly specified baselines tie. On heteroscedastic systems (stochastic Lorenz-63, real air-quality data) the belief's input-dependent variance separates: best single-run NLL on the state and regime tasks, calibration matched only by arms whose NLL it beats, at a fraction of the tuned grids' cost. On the real series the state margin holds across five rolling origins.

Physical human-robot collaboration requires a robot to provide assistance when human intention is clear while remaining compliant when several future motions are plausible. We present an adaptive stiffness framework based on generative action-chunk sampling. Conditioned on an RGB image and external joint-torque estimates, the policy samples multiple future action chunks from an observation-conditioned prior. Variation among the sampled action chunks is used to continuously adapt joint stiffness and damping. Greater variation makes the robot more compliant to facilitate human guidance, whereas lower variation provides firmer assistance. In a real-world collaborative transport task with four possible directions, the proposed method achieved an average success rate of 0.95, compared with 0.83 for a fixed-stiffness ablation and 0.69 for a deterministic baseline. Near direction determination, variation among the sampled action chunks increased and the controller accordingly reduced stiffness. These results suggest that variation among actions sampled by a generative policy can serve as an online control signal for balancing assistance and compliance in physical human-robot interaction.

Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose Stochastic Approximation with Unbiased Simulated Scores (SAUSS), an averaged stochastic approximation based on conditionally unbiased mini-batch score estimates. Each iteration uses a fixed mini-batch regardless of sample size. For multinomial probit, accept-reject sampling provides exact conditional draws and unbiased score estimates for any fixed number of accepted draws. Under local conditions, asymptotic theory for the averaged estimator and the partial-sum process of the SAUSS iterates incorporates mini-batch and simulation variability and supports random-scaling and plug-in inference. In simulations and an application, SAUSS gives comparable results in less than 1% of the computation time of simulated maximum likelihood. SAUSS extends to limited dependent variable models with conditional-expectation score representations and exact conditional sampling.

Functional data analysis is an important statistical field that treats data as random functions. In practice, the random functions are often not fully observed but instead measured at discrete times. While simpler problems, such as mean and covariance estimation, have been widely studied for discretely observed data, optimal estimation of linear regression for this data type has remained unsolved for over two decades. To tackle this fundamental challenge, we propose a novel approach, referred to as pooling ridge estimation, which combines the advantages of pooling strategy and RKHS-based method by incorporating the unbiased estimation of operators based on discretely observed measurements from all subjects. This unified estimation framework enables us to achieve minimax optimality in prediction risk in arbitrary sampling schemes ranging from sparse to dense designs, for both scalar-on-function and function-on-function regression models. Such methodological and theoretical advances are obtained for the first time and accurately reveal the influence of discrete sampling. For scalar-on-function regression, the phase transition occurs once, separating the convergence behavior into two distinct regimes. Remarkably, for function-on-function regression, up to three phase transitions may occur, determined by the sampling frequencies of the predictor/response functions. Finally, simulation experiments and two real data examples provide empirical support for the proposed methods.

High-resolution precipitation fields are essential for hydrological impact assessment, yet global climate model outputs are too coarse and biased for direct use. AI-based statistical downscaling with diffusion models offers a promising approach, but the mechanism by which large-scale atmospheric predictors condition generation remains largely unexplored. We investigate three conditioning strategies for a denoising diffusion probabilistic model applied to daily precipitation downscaling: channel concatenation of upsampled coarse predictors, cross-attention conditioning with a learned convolutional encoder, and cross-attention conditioning with the frozen encoder of the pretrained Prithvi WxC weather foundation model. All strategies are evaluated against an unconditioned baseline under identical conditions using probabilistic, distributional, spectral, and extreme-event metrics for the Colorado River Basin. Concatenation conditioning achieves the lowest point-wise CRPS and MSE, but tends to produce over-smoothed fields that suppress high-intensity events. In contrast, cross-attention conditioning provides substantially better distributional realism and modest improvements in spectral fidelity. Improvements are greatest for extremes: the Prithvi-WxC conditioned model retains over half of >100mm/day events, although estimates are uncertain due to limited samples. When trained on the full dataset, the learned convolutional model performs similarly to the foundation model-conditioned approach while requiring lower computational resources. However, the Prithvi-WxC-conditioned model achieves comparable performance with only five years of training data. These results indicate that cross-attention conditioning offers advantages over simple concatenation for probabilistic precipitation downscaling, and that pre-trained foundation model representations may offer benefits in data-limited settings.

Motivated by parallel decoding in masked diffusion models, we study adaptive parallel sampling of discrete vectors: in each round, a deterministic policy selects unrevealed coordinates on the basis of the values observed so far, and the selected coordinates are sampled independently from their exact conditional marginals. Approximation error is measured by forward Kullback-Leibler divergence, and serial depth is the minimum target-averaged number of rounds meeting a prescribed error budget. Our central result is an exact identity: the divergence of every policy equals the expected conditional total correlation accumulated over its reveal rounds, so conditional total correlation is the exact information cost of within-round parallelism. The identity yields zero-error schedules for finite-order Markov chains with round complexity proportional to the Markov order and logarithmic in sequence length, a matching logarithmic characterization of the Bernoulli walk at every fixed error budget, and a linear-versus-logarithmic separation between left-to-right and hierarchical reveal orders. Uniform random permutations require linearly many expected rounds at every fixed budget; their hard-cap round-error tradeoff is an exact integer-composition problem whose fixed-round asymptotics and joint-scaling frontier we determine. Uniform balanced binary strings have depth of order squared logarithm, and binary one-hot blocks have square-root depth, with rectangular versions realizing every polynomial exponent up to one half. These results separate serial depth from entropy and negative log-likelihood, and establish conditional-dependence structure as a fundamental determinant of parallelizability. Experiments with a masked diffusion language model show that the pseudo-cost distinguishes deployed decoding rules and that its policy rankings agree closely with the quality of self-sampled outputs.

Recent advances in generative AI have significantly increased the demand for high-resolution image and video generation, positioning diffusion models as a core technology. Among them, Diffusion Transformers (DiTs) have emerged as the state-of-the-art (SOTA) models due to their scalability and output quality. However, self-attention in DiTs incurs significant computational overhead, leading to excessively long latency as the complexity grows with the fourth power of the output resolution. While prior works have attempted to mitigate this cost using sparsity and quantization techniques, they fall short of effectively reducing the computational cost in high-resolution DiTs. In this paper, we present APT, a software-hardware co-designed accelerator for high-resolution DiTs. APT leverages attention probabilities as a unified importance metric to jointly optimize computation through fine-grained pruning and adaptive precision scaling. At the algorithm level, we propose Attention Probability-guided Adaptive Dual Thresholding (APDT), which dynamically performs element selection and precision assignment using dual thresholds. To ensure compatibility with memory-efficient FlashAttention, we introduce Timestep-Aware FlashAttention (TAFA), which predicts attention probabilities across timesteps by exploiting temporal similarity. At the architecture level, we co-design a specialized accelerator that efficiently supports irregular sparsity and dual-precision execution, featuring dynamic mask management, address translation, dual-precision compute units, and a tile-based dataflow. Finally, we evaluate APT on SOTA DiT models, including PixArt-$α$, Stable Diffusion 3, and FLUX. APT achieves up to 8.16$\times$ speedup and 14.98$\times$ higher energy efficiency over NVIDIA A100, and up to 3.01$\times$ speedup and 2.04$\times$ higher energy efficiency over EXION, a SOTA diffusion model accelerator.

Correcting flawed reasoning traces remains a significant challenge for Large Language Models (LLMs), whose autoregressive generation can propagate early mistakes into subsequent reasoning. We introduce DCGC, a Masked Diffusion Model (MDM) framework for global correction that uses an imperfect solution draft from an upstream solver as auxiliary context. DCGC combines task-specific Supervised Fine-Tuning (SFT) with a novel inference-time mechanism called Dynamic Dual-CFG. This mechanism separates problem-only and joint problem-draft branches and scales the draft-conditioned residual using a relative confidence gap. Across math, code, and knowledge reasoning benchmarks, DCGC outperforms standard sampling and simpler CFG variants, with additional results suggesting transfer to different diffusion backbones. In test-time setting where ground-truth failure labels are unavailable, DCGC improves full test set accuracy by correcting low-consensus upstream outputs, highlighting its utility as a verifier-free global correction module for difficult reasoning instances.

Multi-teacher on-policy distillation (MOPD) distills several domain-expert teachers into a single student by minimizing per-domain reverse-KL divergence on the student's own rollouts. Existing approaches typically fix the per-domain data mixture before training, overlooking the fact that different domains converge at substantially different rates: some plateau early while others continue to improve throughout the training budget. A fixed mixture therefore wastes compute on fast-converging domains and undertrains slower-converging ones. To address this, we propose D$^3$-MOPD (Dynamic Domain ScheDuling for MOPD), a zero-overhead scheduler that repurposes the per-domain reverse-KL signal already produced during training to adapt the domain mixture online. Running asynchronously outside the training process, an off-process watcher periodically tracks each domain's KL trajectory, estimates remaining headroom and current improvement rate, and accordingly adjusts the domain sampling ratios without altering the core training loop. Our D$^3$-MOPD scales naturally to arbitrary numbers of domains, and the expected benefit grows as more domains introduce more diverse convergence patterns for the scheduler to exploit. On a Qwen3.6-35B-A3B student distilled from four domain-expert teachers, D$^3$-MOPD closes 97% of the average student-to-teacher performance gap, compared with 63% for vanilla MOPD, reaches the same peak performance with an approximately 3$\times$ reduction in rollout steps, and surpasses the specialist teachers on three of seven benchmarks.

Hessian-free high-resolution (HFHR) dynamics augments underdamped Langevin dynamics (ULD) with reversible position diffusion for sampling problems that arise in machine learning. We establish an explicit quantitative contraction rate for HFHR dynamics under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, where the potential function is not necessarily convex. An adapted time-augmented Poincaré inequality yields an explicit rate that improves upon the contraction rate of the underdamped Langevin dynamics. We also give a weak-solution construction and a self-contained spectral proof of the divergence lemma underlying the argument. For HFHR Monte Carlo (HFHRMC) algorithm, which is based on a discretization scheme of HFHR dynamics, we use a path-space Girsanov argument to obtain a non-asymptotic convergence bound and an explicit iteration complexity in total variation distance. The bounds hold for every $α\geq0$ and $γ>0$ and remain regular at the ULD endpoint. Optimizing the iteration complexity bound yields a positive, accuracy-dependent position-diffusion parameter at finite accuracy, while its leading high-accuracy order coincides with that of the optimized ULD endpoint. Our iteration complexity bound improves upon the existing work on HFHR algorithms. Numerical experiments including Bayesian learning problems on real data are provided to illustrate the effect of positive $α$ and its benefit.

We prove the first quantum--classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-βE}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $α=e^{βΔ}$, where $Δ= \max E-\min E$, every classical algorithm---querying the value, gradient, or any higher-order derivatives of the log-density---requires $Ω(α)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrtα\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{Ω(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

Facial attractiveness has been linked to statistical regularities such as symmetry and averageness, suggesting that beauty may depend on the ease with which a face is perceived. We empirically test this hypothesis by training variational autoencoders on four face datasets without attractiveness supervision and evaluating their representations on the 597 faces from the Chicago Face Database. Across models, human attractiveness ratings closely aligns with the direction defined by the VAE evidence lower bound (ELBO) in rate-distortion space. Independently learned latent spaces contain an attractiveness direction that transfers strongly across random initializations and training data. We also find that attractive faces are more prototypical in both shape and latent space. Our results connect classic accounts of aesthetics with learned generative models and provide empirical support for a variational interpretation of the processing fluency theory of aesthetic pleasure.

Generative models are commonly ranked by Fréchet Inception Distance (FID) and Kernel Inception Distance (KID), yet FID's first-two-moment summary can miss distributional differences, and a reported scalar gap alone is not a calibrated test against sampling variation. FID's moment restriction has concrete consequences: on ImageNet, visually unrecognizable images optimized only to match the reference Inception mean and covariance obtain FID $24.7$ versus $58.6$ for held-out real images (lower is better). Moreover, FID and KID are scalar discrepancies that are unchanged when the two samples are exchanged and therefore do not encode the direction of a dispersion change: under-dispersion, as can occur in mode collapse, versus over-dispersion. We introduce ZID (Z-resolved Integrated Diagnostic), which combines six standardized location- and dispersion-sensitive arms from a rank graph (RISE) and Gaussian kernels (GPK at two bandwidths). Rather than asking one scalar to serve incompatible roles, ZID reports three linked outputs: an index for ranking departure magnitude, a permutation $p$-value for testing distributional equality, and a signed dispersion readout for diagnosis. In controlled experiments, ZID detects a broad range of departures, and its score tracks increasing severity along the corresponding sweeps, including cases in which FID is flat or reversed. On DiT-XL/2 and SiT-XL/2 guidance sweeps, ZID detects departure from real data, and its signed readout labels the high-guidance diversity collapse as under-dispersion.