生成模型理论与方法

Outliers can substantially distort Gaussian process regression (GPR) due to its conventional Gaussian observation likelihood, leading to inaccurate model learning and prediction. To address this limitation, this article introduces a generative GPR model that captures observation-specific contamination and adaptively mitigates the influence of outliers. Subsequently, a variational generalized expectation-maximization procedure is used to learn the latent variables and GPR model parameters. Experiments on synthetic and real datasets under different contamination settings demonstrate that the proposed method remains competitive with-and in several cases outperforms-robust GPR baselines in prediction accuracy. Moreover, the proposed method shares the cubic computational scaling of the compared GPR methods.

Statistical inverse problems have garnered significant attention in recent years due to the growing importance of statistical learning theory and functional analytic approaches in the fields of machine learning and artificial intelligence. In this paper, we investigate the stable approximation of the element $u^{\dagger}$ that satisfies the equation $Au = g$, where $A$ is a linear operator that maps a Banach space into an appropriate function space. The function $g$ is observed only through independently and identically distributed data points that are corrupted by noise and assumed to follow an unknown distribution $ρ$. We employ the Tikhonov regularization scheme, leveraging statistical learning techniques and the framework of reproducing kernel Banach spaces to estimate the solution. We establish convergence and derive the convergence rate of the estimated solution with respect to the true solution as the number of data points increases, with the rate expressed in probabilistic terms. The theoretical findings are further supported by numerical experiments that demonstrate the effectiveness of the proposed approach.

Inference-time quality-enhancement methods are an effective and widely adopted means of improving diffusion models without expensive retraining. We study a family of training-free techniques conceptually rooted in Classifier-Free Guidance (CFG), most of which were originally proposed on older U-Net diffusion models and validated using metrics that assess image quality in isolation, without accounting for compositional alignment or semantic correspondence between the generated image and its associated text prompt. We re-evaluate eight such methods on two open-weight rectified-flow transformers under a fixed per-model protocol and three compositional-alignment benchmarks. No method consistently improves on CFG across the measured criteria. APG obtains several nominal best scores, but the corresponding gains often remain within the estimated evaluation uncertainty. Attention-perturbation methods provide isolated gains on SD3.5 Medium and more frequent degradations on FLUX.2 [klein] 4B Base, while CFG remains a competitive lower-cost baseline.

This paper investigates an increasingly important topic in generative modeling: pixel-space diffusion models. Although numerous studies have explored this topic, most focus on small-scale or class-conditional settings. Consequently, a practical recipe for training pixel-space models that rival or exceed well-established latent-space counterparts remains elusive. Through a comprehensive empirical study, we first observe that direct large-scale pre-training in pixel space converges substantially more slowly than in latent space. This observation motivates a latent-to-pixel strategy that acquires generative priors efficiently in latent space and transitions to pixel space during post-training. We then systematically investigate the key design choices governing this transition, including weight initialization, data composition, prediction target, decoder architecture, and noise schedule, and identify a practical recipe that makes the resulting pixel-space models match or outperform their latent-space counterparts while delivering 3.18 to 4.75 times end-to-end inference speedups. We hope that our findings provide useful empirical insights and practical guidelines for future research on pixel-space generation.

Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.

Diffusion and flow matching models have made significant progress in text-to-image generation, yet high computation, quadratic complexity, and large memory footprint hinder high-resolution synthesis and edge deployment. We propose Nexus, which integrates sparse architecture, linear complexity, and low-bit quantization. It combines MoE feed-forward layers, gated DeltaNet attention, and per-expert low-bit training to reduce computation and memory. Their joint optimization allows Nexus to achieve generation quality comparable to mainstream models such as SDXL and SD3 while delivering markedly higher inference efficiency. Experiments on COCO and LAION validate its effectiveness.

Machine unlearning (MU) aims to remove the influence of specific training data while preserving model utility. As the name suggests, MU can be viewed as the inverse of learning, using gradient-based updates to reduce the influence of a forget-set by counteracting the previously learned behavior. Recently, Muon, a gradient descent variant, has been introduced. Muon applies spectral magnitude normalization to encourage exploration of rare directions and demonstrates promising performance. Inspired by Muon, we adopt the spectral view for unlearning and propose Spectral Saliency Unlearning (SSU). SSU thresholds weak singular components and updates only those directions supported by a confident unlearning signal. We further provide theoretical justification for this thresholding approach from the perspective of the forgetting-retention trade-off. Experiments across image classifiers, diffusion models, and LLMs demonstrate SSU's effectiveness.

Deciding whether a Sokoban puzzle is solvable is PSPACE-complete (Culberson, 1997): solutions can be exponentially long and there is no short certificate to check. Solvability is also a fragile property, since even a single misplaced wall can silently render an entire puzzle unsolvable. In this work, we show that a transformer-based discrete diffusion model trained purely on tile completion, with no access to solvers, rewards, or solvability labels, achieves a solvability rate of 77.4%, with 94.5% of the remaining failures rendered solvable by removing a single wall. In other words, a global, search-heavy property follows from a local training objective: trained only to fill in masked cells, the model inherits solvability it was never trained on. An autoregressive model factorizes as $p(c_k \mid c_1 \dots c_{k-1})$, meaning a fixed order, always conditioned on a prefix. Masked diffusion does not: it hides a random subset of cells and learns $p(c_k \mid \text{any subset})$, so at generation time it can reveal cells in any order, each one conditioned on everything already placed, wherever it sits on the board. A puzzle's difficulty comes from exactly this kind of non-local interaction, a decision in one part of the grid constraining what will work somewhere else entirely. A generator that is not locked into a single fixed order is therefore a better structural match for the problem than one that is. The training pipeline is adapted from MD4 (Shi et al., 2024) and the dataset is DeepMind's Boxoban (Guez et al., 2019). The trained model and instructions for generating puzzles are publicly available.

Current flow matching models learn to transport the source i.i.d. Gaussian noise into the target distribution of natural images, yet this source distribution carries no notion of spatial structure. Images however are fundamentally local since nearby pixels are strongly correlated. By sampling the noise independently, we hypothesize that models are implicitly encouraged to exploit less noisy neighbors as context during training, partially bypassing the need to properly learn the true local structure of images. The source distribution, in other words, works against the inductive bias of the image domain. To ameliorate this design discrepancy, we propose StructFlow which encodes spatial locality directly into the source by having the pixels within a small region share a common noise component. This structured source produces transport paths that are geometrically aligned with image regions - enabling properties that generic flow matching struggles to provide: fine-grained local editing that naturally respects boundaries, robust structure preservation, and smooth semantic interpolation between images. We show that these benefits also extend to large pre-trained models, demonstrating that StructFlow can even be incorporated through a lightweight post-training phase. Comprehensive experiments on multiple datasets, in unconditional, class and text-conditioned regimes, using different diffusion transformer architectures confirm that StructFlow not only offers competitive image generation quality, but also significantly improves localized controllable re-synthesis.

Text-to-image diffusion models can be misused to generate harmful content through adversarial or paraphrased prompts that bypass built-in safety mechanisms. Existing concept erasure methods often suffer from limited robustness against adversarial prompts, degradation of benign generation quality, or reliance on inference-time interventions that introduce persistent computational overhead. To address these limitations, we formulate concept erasure as a domain alignment problem in the text representation space. We propose a lightweight Text Encoder Alignment framework (TEA) that fine-tunes only the text encoder while keeping the generative backbone fully frozen. Given concept--anchor prompt pairs, our method trains a discriminator to distinguish token-level representations of concept-containing prompts from those of safe anchor prompts, while updating the text encoder to make these representations indistinguishable. TEA introduces zero inference-time overhead and requires only a small number of fine-tuning steps, making it highly efficient to deploy at scale. Despite this efficiency, TEA achieves state-of-the-art erasure robustness against black-box and white-box adversarial attacks on Stable Diffusion v1.4, while preserving generation quality on benign prompts. Furthermore, TEA is model-agnostic and achieves the lowest attack success rate on Stable Diffusion v3.5, extending concept erasure to a Rectified Flow Transformer architecture with T5 conditioning where prior methods remain largely unexplored. Code is available at \href{https://github.com/alirezafarashah/TEA.git}{https://github.com/alirezafarashah/TEA.git}

Although text-to-image generative models produce impressive results, they struggle to generate densely detailed, high-resolution (HR) images. Current literature addresses this issue with a low-to-high-resolution approach. First, a low-resolution (LR) image is generated. Then, an upsampled version is generated using the LR image as an additional cue. In this paper, we present Joint Latent Trajectories (JoLT). To generate an image, JoLT uses two streams that jointly denoise LR and HR latent images at each sampling step. The LR latent controls the overall layout, while the HR latent controls the details. We interconnect both branches to jointly integrate their information. We extensively validate our method, demonstrating its advantages over competing baselines. The resulting images are not only richly detailed but also visually pleasing, opening new avenues for artistic creation.

Multimodal data collected by heterogeneous devices are used for collaborative training, where federated learning (FL) serves as a key paradigm for effective distributed modeling with data privacy preservation. However, local training suffers from the forgetting of previously learned global knowledge under cross-client data heterogeneity, which leads to significant declines in both performance and convergence speed. Most previous studies rely on global alignment strategies to retain global knowledge, which hinder local optimization and lead to inadequate supervision of missing classes. Some studies introduce proxy datasets to supplement supervision for missing classes. However, it remains a challenge to balance class-wise global consistency and local optimization objectives without proxy datasets. In this work, we propose FedADB, a Class Anchor-Driven Dual-Branch FL framework. Specifically, the server generates class anchors optimized in a differentiable input space, which are shared across clients. These class anchors serve as global references that provide supervision for missing classes during local training. A dual-branch collaborative training mechanism is designed for clients. In this mechanism, the anchor-based global branch focuses on learning with global consistency, achieving global knowledge alignment by class-anchor balanced sampling. The local calibration branch focuses on learning discriminative local features, mitigating the degradation of local representations caused by excessive global alignment. Extensive experiments across multiple medical and natural datasets demonstrate that FedADB achieves significant improvements in both accuracy and convergence speed.

Generative model alignment has received broad interest, and significant progress has been made in supervised fine-tuning and inference-time computation. Yet, alignment has remained poorly understood from a statistical learning perspective. We formulate inference-time alignment as a weak-to-strong learning problem, where a reference policy (weak learner) is assumed to be fairly good and the goal is to produce a strong learner that predicts a good response at test time with arbitrarily high probability. Our problem is formulated as learning from scratch --- everything is learned from data rather than assuming access to a good reward estimate, and thus differs from the existing inference-time alignment theory. Our model shares similarity to the recent work of arXiv:2510.15464, where for each prompt, there could be multiple good responses. Our definition of the alignment learnability follows the PAC learning principle. We introduce a novel combinatorial dimension of the reward class which we call the alignment dimension, and show that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite. The core of our learning procedure works by invoking the ordinary one-inclusion graph algorithm to run a tournament over all pairs of label sets satisfying that neither is a subset of the other. We believe our results might shed light on establishing a complete theoretical understanding towards alignment.

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

The alternating direction method of multipliers (ADMM), as a landmark algorithm, has attracted tremendous research attention and extensive practical applications over the past two decades. It is well known that, although the two-block ADMM enjoys well-established theoretical convergence guarantees, its direct extension to the three-block case may fail to converge, as demonstrated by existing counterexamples [5]. However, to the best of our knowledge, the case in which the third constraint block is the identity remains unresolved: the existing literature gives neither a general convergence proof nor a counterexample for this subclass. In this paper, we give a negative answer: direct three-block ADMM may fail even when the first two blocks are strongly convex quadratics. Using Codex with GPT-5.6 Sol, we construct an explicit rational counterexample candidate and verify it along a piecewise-affine reduction path; exact checks show that direct three-block ADMM on this instance produces a bounded nonconvergent orbit of period 66. Within the same Codex workflow, we further guide a study of multiplier relaxation and clarify when convergence can be restored at the fixed-instance and class levels: a problem-dependent small dual step can restore convergence, whereas no positive relative step works uniformly over the whole class. Furthermore, we also test the recent Kimi Code with Kimi K3 model without the Codex candidate or project-specific route guidance; along a different path it produces an exact locally attracting period-23 certificate, convertible to an equivalent all-identity instance. The comparison suggests that different research-harness configurations can shape the mathematical objects explored and the certificates pursued.

Smart manufacturing processes are often installed with a large number of sensors, imaging devices and computers, which not only enable instant communication across various modules of a production system but also aid in intelligent manufacturing management. In this paper, we introduce MODERN, a deep learning framework for quality monitoring and fault isolation, which integrates these enhanced capabilities into the practice of industrial quality control. Using the architecture of an inception residual neural network, we develop a control chart that monitors the likelihood of a product containing defects. We also propose a faulty region estimator that identifies the defective area using transfer learning. To extend our framework to cases where there are not sufficient training data, we suggest a transfer monitoring technique that requires only a small sample size and a hypothesis testing approach for quantitatively assessing the applicability of our method. Theoretically, we establish the minimax optimal convergence rate for both our defect likelihood estimation and fault diagnosis. Our results lead to a seemingly counter-intuitive managerial implication - it may not always be in a manufacturer's best interests to keep upgrading its monitoring equipment regardless of the cost. Empirically, we demonstrate the superior performance of our method in comparison with a state-of-the-art approach using both simulated experiments and real data.

Diffusion models have achieved impressive results in image, video, and streaming generation. However, compared to traditional 3D rendering, they still lack precise control over the generated output. We believe a viable path forward is to use generative models as learned renderers conditioned on traditionally rendered G-buffers. We introduce RGBX-Next, a unified generative framework for forward and inverse rendering, which allows estimating G-buffers from images, videos, and streams, and rendering realistic images, videos, and streams from G-buffers. Our key contribution is a general recipe for finetuning diffusion transformer (DiT) models into generative forward and inverse renderers. We show that the resulting models achieve high quality in both realistic generative rendering and intrinsic decomposition. We will make all our models publicly available. We believe that the design principles presented in this paper will benefit future research on controllable generative forward and inverse rendering.

Diffusion models offer a natural way to model uncertainty in time series forecasting, yet their iterative sampling process is often treated as a uniformly beneficial refinement procedure. Our study challenges this view by examining how forecast quality evolves throughout reverse diffusion. We find that general temporal structure is often recovered at relatively high noise levels, whereas continued low-noise refinement can introduce statistical drift and degrade the final forecast. Our analysis further suggests that this behavior explains why prior methods often favor relatively narrow diffusion architecture and schedule design. Building on this observation, we propose a label-free global stopping criterion that detects the optimal termination point, eventually speeding up inference and improving predictive accuracy. Additionally, since early stopping terminates inference in high-noise regions, we propose a Bernoulli timestep sampler that concentrates training on this region while preserving coverage of the full diffusion process. Extensive experiments conducted across eight real-world datasets demonstrate the superior performance of our method compared to existing approaches.

Power Sampling sharpens a language model's distribution over complete generation trajectories, offering a verifier-free way to improve reasoning at inference time. It also has the potential to serve as a general-purpose front end for a broad range of downstream sampling methods. However, we uncover a striking paradox: Power Sampling can drive more probability mass toward correct trajectories while degrading the downstream inference it is intended to enhance. Using self-consistency as a representative case, we observe accuracy drops of up to 18.5 percentage points across models and reasoning benchmarks. We trace this paradox to two mismatches. Dose mismatch arises because a fixed exponent induces drastically different amounts of distributional change across problems. Coverage mismatch arises because global sharpening concentrates mass on a narrow set of dominant paths: high pass@k, often interpreted as evidence of preserved diversity, can therefore coexist with the loss of broad reasoning-path support required for downstream aggregation, search, and selection. Guided by this diagnosis, we replace uniform trajectory exponentiation with a deformation-controlled, support-preserving Power target that calibrates sharpening across problems while limiting the suppression of moderate-probability paths. In a same-budget instantiation with weighted self-consistency, the repaired sampler reverses the losses caused by global Power and outperforms standard multi-sample inference across reasoning benchmarks.

In offline RL, estimating the optimal action-value function $Q^*$ can be formulated as solving the optimal Bellman equation based solely on offline observations. A fundamental challenge is that the reward function and transition kernel are unknown, so the optimal Bellman operator is not directly observable from data. To address this issue, we propose a novel framework that decouples operator estimation from value function learning. In this approach, we first formulate conditional diffusion models to estimate the reward law and transition kernel, which induces a data-driven approximation of the optimal Bellman operator. We then plug these estimators into the Bellman equation and obtain a deep estimator of $Q^*$ by minimizing the empirical Bellman residual over a neural network function class. Theoretically, we first establish sharp nonasymptotic convergence rates for learning the optimal Bellman operator through an end-to-end analysis of conditional diffusion estimation in total variation distance. We then establish the oracle value-stage rate $\widetilde{\mathcal O}\bigl(n^{-\frac{2β}{d_x+d_a+2β}}\bigr)$ for the excess Bellman residual risk. Finally, under a concentrability condition, we translate this residual bound into an $L^2$ convergence rate of $\widetilde{\mathcal O}\bigl(n^{-\fracβ{d_x+d_a+2β}}\bigr)$ for the resulting deep estimator of $Q^*$, where $d_x$ and $d_a$ denote the dimensions of the state and action spaces, respectively, and $β$ denotes the Hölder smoothness index of $Q^*$. Importantly, our theoretical analysis does not rely on completeness assumptions commonly used in deep RL theory. Extensive numerical experiments demonstrate the effectiveness of the proposed method and its strong empirical performance.

Iterative Generative Models (IGMs) span autoregressive and diffusion paradigms, and hybrid variants that couple them can achieve remarkable image-generation fidelity. However, their iterative inference incurs substantial computational overhead, making Post-training Quantization (PTQ) appealing for acceleration, while directly applying vanilla PTQ to hybrid IGMs can trigger model collapse. By analyzing these failures, we identify two critical challenges: Excessive Outliers (EOs) in the activations create an irreconcilable trade-off between preserving normal precision and covering EOs, resulting in severe degradation in generation quality; Amplified Anomalies (AAs) arising unpredictably from minor quantization errors, create a mismatch between calibration and inference, thus iteratively triggering model collapse. To address these challenges, we introduce HyGenQ, a PTQ framework for hybrid IGMs. HyGenQ comprises Hierarchical Cluster Decoupling (HCD) and Scaling Recalibration (SR). HCD identifies and decouples outlier channels via a multi-stage clustering process, effectively isolating EOs while maintaining normal value precision, thereby alleviating performance degradation. SR scales AAs beyond Gaussian Bound, thereby avoiding model collapse caused by aggressive truncation. Extensive experiments demonstrate that HyGenQ successfully quantizes representative hybrid IGMs to 8-bit precision (W8A8), significantly outperforming existing baselines and validating its robustness across different model families.

I document an ideologically asymmetric break in the pre-existing diversification trend of political discourse, emerging around late 2022, using 6 million Reddit comments from two cross-partisan forums, 2019-2025. Conservative users experienced an interruption of their prior diversification trajectory; progressive users showed no comparable change. The asymmetry is consistent across estimation strategies (ITS, DiD, RDiT, propensity-score matching) and temporal aggregations. A daily-frequency permutation test over 2,377 candidate cutoff dates shows the ChatGPT threshold produces an unremarkable estimate (49.8th percentile): the shift builds gradually instead of breaking at a single date. A continuous cumulative LLM index, tracking AI exposure across seven model releases, remains significant under a quadratic trend specification that eliminates the binary estimate. A stayer analysis narrows the mechanism: the homogenization effect disappears when the sample is restricted to authors active throughout the study period, and the stayer confidence interval excludes within-author effects even a tenth the size of the full-sample estimate. The mechanism is most parsimoniously ecological (community-level discursive convergence) rather than individual-level AI adoption, though the data cannot cleanly separate this account from concurrent secular change.

Physics-constrained diffusion for high-contrast, sharp-interface multiphase fields faces three coupled difficulties. At coefficient jumps, expanded pointwise strong-form PDE residuals contain singular gradient terms that can penalize physical interfaces. Under extreme contrast, low-magnitude phases may fall below the diffusion noise floor and be erased, misscaled, or generated with negative coefficients, while a global likelihood scale allows high-magnitude phases to dominate supervision. We therefore propose Multiphase-Diff, which makes three corresponding contributions: (i) a conservative flux residual that avoids differentiating discontinuous coefficients and enforces discrete conservation; (ii) an analytic bijective representation that maps low-amplitude signals to order-one latent scales and guarantees coefficient positivity through exponential decoding; and (iii) a Jacobi-preconditioned likelihood that normalizes local residual scales for balanced supervision. Experiments on three complementary multiphase benchmarks demonstrate the superiority of Multiphase-Diff over seven baselines in both physical and distributional fidelity and its robustness across phase contrasts and compositions, establishing its effectiveness for scientific sample generation in this challenging regime.

Text-Image-to-Video (TI2V) models are an emerging unified architecture, where a single model simultaneously supports text-to-video (T2V) and image-to-video (I2V) generation. Given a high-quality first frame or a detailed textual prompt, TI2V models unlock substantially better visual quality than their T2V mode, raising a natural question: can the capability elicited by such privileged conditions be internalized into the model's own base generation ability? A common approach toward this goal is model self-distillation. However, the most straightforward solution, supervised fine-tuning, follows an off-policy strategy: its supervision is confined to teacher-generated endpoints from a fixed offline distribution rather than student-visited states, lacking precise correction tailored to the evolving policy. Recent on-policy distillation methods instead suffer from condition-state mismatch, where supervision is steered toward the given first frame instead of the student's actual content, misleading the correction. To achieve self-distillation that absorbs the teacher's privileged prior while retaining precise policy correction, in this work, we propose Hybrid-Policy Self-Distillation (HPSD), a novel self-distillation framework where a single TI2V model acts as both teacher and student under different conditions: the teacher operates in TI2V mode with a high-quality first frame and an enhanced prompt, while the student runs in the base T2V mode with only the vanilla prompt. Specifically, the student inherits off-policy teacher trajectory points as anchors, locally refines them toward its own policy, and finally receives velocity-level supervision on these self-generated roll-outs. Extensive experiments demonstrate that HPSD significantly improves T2V performance while also delivering notable TI2V gains, effectively strengthening the model's base generation ability.

Blue-noise sampling is widely used in computer graphics, but existing methods separate statistical modeling from scalable generation. Optimization and transport methods produce high-quality point sets by coupling all samples together. Procedural and tile-based samplers are local, but define their output only implicitly. We formulate blue-noise generation as sampling from a Gibbs distribution over binary lattice occupancies with pairwise repulsive interactions. Density, repulsion strength, interaction scale, and kernel hardness are parameters of this distribution. Because the energy sums over pairs, distant interactions can be dropped with a bounded change to the distribution, leaving a Markov random field of bounded degree. To sample it, we trace the Markov chain backward from the state we want, following Coupling Towards The Past, and cut the trace at a fixed depth. This bounds the cost, and it bounds the region each sample depends on. A tile generated on its own, with a sufficient halo, is then bit-identical to the same region generated on any larger domain, in any order and with no communication between tiles. Memory is set by the tile size, not by the output size, and accuracy is traded against cost through parameters with a proven error bound rather than by switching algorithms. We validate the model, the sampler, and these guarantees separately. The ensemble reproduces standard blue-noise spectra and moves continuously between them as its parameters vary. The sampler matches its predicted work and memory. Tiled output is verified bit-identical to full-domain generation. We demonstrate adaptive stippling at 14K, where existing methods need memory proportional to the output, along with multi-class extensions.

Geometry-conditioned multi-view diffusion enables high-quality 3D texture generation, but its repeated per-view denoiser evaluations introduce substantial computational cost. Existing training-free accelerators primarily exploit temporal redundancy by reusing computation across denoising steps. In multi-view texturing, however, skipping a step also removes the cross-view interaction that continually aligns different observations of the same surface, leading to rapidly degraded consistency and fidelity. Our analysis identifies a complementary source of redundancy: although intermediate features remain view-specific, geometrically corresponding surface points exhibit transferable evolution in their predicted clean signals. Based on this observation, we introduce \gc{}, a training-free plugin that evaluates a rotating subset of anchor views and transports their geometry-aligned per-step $\xz$ updates to the remaining views. Periodic full-view computation controls accumulated error, while sampler-consistent reconstruction preserves the denoising trajectory. \gc{} requires neither retraining nor architectural modification and uses the position maps already available in geometry-conditioned texturing pipelines. Across Hunyuan3D-2.1, SyncMVD, and MVPainter, \gc{} achieves a stronger speed--fidelity trade-off than temporal caches and step reduction at operating points above $2\times$. On Hunyuan3D-2.1, it delivers a $2.21\times$ denoiser-loop speedup with an MV-LPIPS of 0.0293 and an MV-PSNR of 33.60 dB, providing the best fidelity among all tested methods above $2\times$. The same transferred configuration reaches the highest speedup and lowest FLOPs on SyncMVD, while \gc{} achieves the lowest FLOPs and best fidelity among the accelerated methods on MVPainter. These results establish cross-view geometry as an effective acceleration axis for multi-view texture diffusion.

Generating crystals has recently attracted significant interest due to their broad applications in materials science. However, existing generative models struggle to produce complete crystallographic specifications, limiting their ability to capture global symmetry and structural dependencies. In particular, current state-of-the-art approaches generate crystals only up to site symmetries and rely on sampling space groups from empirical distributions during generation. Inspired by spontaneous symmetry breaking in physics, where crystals break symmetries under external conditions, we propose a novel diffusion-based framework that generates full structure specifications by reversing from the lowest-symmetry priors. Our method leverages a Markovian jump-diffusion process to model these symmetry-breaking dynamics, enabling it to traverse different space groups in a physically motivated manner. Our model, dubbed Symmetry-breaking Crystal Diffusion (SbCD), introduces a principled approach to explicitly incorporate inter-space-group transitions into the generative process. In de novo generation experiments on MP20 and MPTS-52, SbCD outperforms its symmetry-preserving counterpart by a substantial margin, offering a promising perspective for generative modeling of crystalline materials.

Post-click conversion rate (CVR) is a key metric in various scenarios including e-commerce and advertising, reflecting the efficiency and user experience in the second stage of the conversion process. Estimating the causal effect on CVR is therefore of great practical importance. However, directly applying existing causal inference methods to clicked samples introduces sample selection bias and increased variance due to the exclusion of non-click data. Recent studies on CVR prediction introduce "ideal loss", which optimizes model parameters using an unbiased estimate of the loss over the full sample. Nevertheless, there is no guarantee that unbiasedness of the loss implies unbiasedness of the final estimator. We revisit this challenge from the perspective of semiparametric theory. Specifically, we develop a new doubly robust causal effect estimator for chain-structured outcomes such as CVR, and derive its theoretical properties in detail. It achieves a faster convergence rate compared to nuisance parameters estimation and is therefore more robust when using flexible nonparametric estimators, including neural networks. Based on these theoretical findings, we further design a framework based on targeted regularization to improve numerical stability and practical applicability. Extensive experiments on synthetic and real-world data demonstrate the effectiveness and robustness of our method. In addition, we find that naively combining loss debiasing with standard causal estimators underperforms our method, highlighting the necessity of developing the new estimator tailored to this CVR-style objective with solid theoretical guarantees.

We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j). The core technical contribution is the Sinkhorn linearization — the implicit-function sensitivity of the entropic OT plan to the cost — together with its spectral proxy, a formula that is spectrally exact yet geometrically transparent. The restricted Hessian on the tangent space satisfies the spectral sandwich (pi_min/epsilon) I <= H_T^{-1} <= (pi_max/epsilon) I, yielding the single core bound sigma_min >= (pi_min/(a_max epsilon)) sqrt(lambda_min(Sigma)) that drives the entire theory. On this core we establish four theorems and one observation. T1 (identifiability): theta is globally injective on the quotient of the gauge kernel, with dimension bound F <= (K-1)^2. T2 (sparsistency): the l1-penalized estimator recovers the true support under irrepresentability and score concentration, with exponential failure probability. T3 (well-posedness): the feature-moment map M(theta) = Phi^T x_theta is strongly monotone, and the inverse is Lipschitz with constant L <= epsilon ||Phi^T S_a||_op / (pi_min lambda_min(Sigma)). T4 (convergence): local strong convexity with mu >= pi_min^2 lambda_min(Sigma) / epsilon^2 guarantees monotone gradient descent convergence. O5 (misspecification): the estimator converges to the OT-model projection of the truth; the Holder continuity of the projection map is assessed numerically, yielding setting-dependent empirical exponents alpha_eff in (0,1).

Limit order book (LOB) simulators are most useful to practitioners when they combine realistic market dynamics, computationally efficient sampling, controllable scenario generation, and the ability to generalize beyond the instruments seen during training---properties that existing agent-based and deep generative simulators provide only partially. We present FlowLOB, a conditional flow-matching generator of LOB trajectories, trained on multiple Hong Kong Exchange (HKEX) symbols at three sampling frequencies ($0.1$s, $1$s, $10$s) in tick-relative representation that transfers to unseen instruments. Because flow and diffusion models admit a common formulation, we train both with identical data, architecture, and budget, and sample both through the same fixed-step ODE solvers, yielding a controlled comparison of sampling efficiency and fidelity. Flow matching attains its best quality with only $10$ ODE-solver steps, whereas diffusion needs many more function evaluations to approach the same fidelity. At this efficient operating point, FlowLOB improves realism over baselines, two learned and two agent-based models, in most distributional metrics at the two finer sampling frequencies. We evaluate counterfactual controllability with a distributional test that asks whether changing a scenario condition moves the generated statistic toward the corresponding real tail regime; FlowLOB satisfies this criterion in most tested settings. Both realism and control effects transfer zero-shot on a held-out symbol. We additionally conduct ablation studies on the network architecture and the learning rate.