Deep Vision in Smart Manufacturing: MODERN Framework for Intelligent Quality Monitoring and Diagnosis

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.

Offline Deep Q* Estimation with Diffusion Models

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.

Conditional Diffusion for Nonparametric Instrumental Variable Quantile Regression

This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation. In the first stage, we estimate the joint conditional distribution of the outcome and endogenous covariates given the instrument using a variance-preserving conditional diffusion model. In the second stage, we approximate the conditional moment operator through Monte Carlo sampling and a kernel-smoothed surrogate for the indicator function, and then estimate the structural quantile function by empirical risk minimization over deep neural networks. We establish an excess-risk bound for the proposed estimator and derive end-to-end total variation guarantees for the conditional diffusion model under unbounded support, explicitly accounting for score estimation, early stopping, and discretization errors. Our theory is developed under a polynomial-tail envelope on the data distribution and degenerates continuously to the exponential setting: as the tail index grows, the obtained excess-risk rate converges to the minimax-optimal rate of nonparametric regression, thus our heavy-tailed theory covers the classical light-tailed nonparametric guarantees as a limiting case. Simulation studies and a real-data application demonstrate that the proposed method outperforms existing nonparametric IVQR approaches, with gains that become increasingly pronounced as the dimensionality of the covariates and instruments increases.

Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations

Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

Deep Bootstrap

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given the covariates. This model is then used to generate bootstrap samples by pairing the original covariates with newly synthesized responses. We reformulate nonparametric regression as conditional sample mean estimation, which is implemented directly via the learned conditional diffusion model. Unlike traditional bootstrap methods that decouple the estimation of the conditional distribution, sampling, and nonparametric regression, our approach integrates these components into a unified generative framework. With the expressive capacity of diffusion models, our method facilitates both efficient sampling from high-dimensional or multimodal distributions and accurate nonparametric estimation. We establish rigorous theoretical guarantees for the proposed method. In particular, we derive optimal end-to-end convergence rates in the Wasserstein distance between the learned and target conditional distributions. Building on this foundation, we further establish the convergence guarantees of the resulting bootstrap procedure. Numerical studies demonstrate the effectiveness and scalability of our approach for complex regression tasks.

Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs

We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability-flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the flow ODE. For both applications of the Langevin diffusions, we establish convergence guarantees. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks.

Inference-Time Alignment for Diffusion Models via Doob's Matching

Inference-time alignment for diffusion models aims to adapt a pre-trained diffusion model toward a target distribution without retraining the base score network, thereby preserving the generative capacity of the base model while enforcing desired properties at the inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce Doob's matching, a novel framework for guidance estimation grounded in Doob's $h$-transform. Our approach formulates guidance as the gradient of logarithm of an underlying Doob's $h$-function and employs gradient-penalized regression to simultaneously estimate both the $h$-function and its gradient, resulting in a consistent estimator of the guidance. Theoretically, we establish non-asymptotic convergence rates for the estimated guidance. Moreover, we analyze the resulting controllable diffusion processes and prove non-asymptotic convergence guarantees for the generated distributions in the 2-Wasserstein distance.

Provable Diffusion Posterior Sampling for Bayesian Inversion

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a warm-start strategy to initialize the particles. To approximate the posterior score, we develop a Monte Carlo estimator in which particles are generated using Langevin dynamics, avoiding the heuristic approximations commonly used in prior work. The score governing the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior distribution. On the theoretical side, we provide non-asymptotic error bounds, showing that the method converges even for complex, multi-modal target posterior distributions. These bounds explicitly quantify the errors arising from posterior score estimation, the warm-start initialization, and the posterior sampling procedure. Our analysis further clarifies how the prior score-matching error and the condition number of the Bayesian inverse problem influence overall performance. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method across a range of inverse problems.

CRPE: Expanding The Reasoning Capability of Large Language Model for Code Generation

We introduce CRPE (Code Reasoning Process Enhancer), an innovative three-stage framework for data synthesis and model training that advances the development of sophisticated code reasoning capabilities in large language models (LLMs). Building upon existing system-1 models, CRPE addresses the fundamental challenge of enhancing LLMs' analytical and logical processing in code generation tasks. Our framework presents a methodologically rigorous yet implementable approach to cultivating advanced code reasoning abilities in language models. Through the implementation of CRPE, we successfully develop an enhanced COT-Coder that demonstrates marked improvements in code generation tasks. Evaluation results on LiveCodeBench (20240701-20240901) demonstrate that our COT-Coder-7B-StepDPO, derived from Qwen2.5-Coder-7B-Base, with a pass@1 accuracy of 21.88, exceeds all models with similar or even larger sizes. Furthermore, our COT-Coder-32B-StepDPO, based on Qwen2.5-Coder-32B-Base, exhibits superior performance with a pass@1 accuracy of 35.08, outperforming GPT4O on the benchmark. Overall, CRPE represents a comprehensive, open-source method that encompasses the complete pipeline from instruction data acquisition through expert code reasoning data synthesis, culminating in an autonomous reasoning enhancement mechanism.

Boosting Statistic Learning with Synthetic Data from Pretrained Large Models

The rapid advancement of generative models, such as Stable Diffusion, raises a key question: how can synthetic data from these models enhance predictive modeling? While they can generate vast amounts of datasets, only a subset meaningfully improves performance. We propose a novel end-to-end framework that generates and systematically filters synthetic data through domain-specific statistical methods, selectively integrating high-quality samples for effective augmentation. Our experiments demonstrate consistent improvements in predictive performance across various settings, highlighting the potential of our framework while underscoring the inherent limitations of generative models for data augmentation. Despite the ability to produce large volumes of synthetic data, the proportion that effectively improves model performance is limited.