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Deep Learning · Generative Models and Autoencoders

Shikang Zheng, Guantao Chen, Qinming Zhou, Yuqi Lin, Lixuan He, Chang Zou, Peiliang Cai, Jiacheng Liu, Linfeng Zhang

Diffusion Transformers offer state-of-the-art fidelity in image and video synthesis, but their iterative sampling process remains a major bottleneck due to the high cost of transformer forward passes at each timestep. To mitigate this, feature caching has emerged as a training-free acceleration technique that reuses hidden representations. However, existing methods often apply a uniform caching strategy across all feature dimensions, ignoring their heterogeneous dynamic behaviors. Therefore, we adopt a new perspective by modeling hidden feature evolution as a mixture of ODEs across dimensions, and introduce \textbf{HyCa}, a Hybrid ODE solver inspired caching framework that applies dimension-wise caching strategies. HyCa achieves near-lossless acceleration across diverse tasks and models, including 5.55$\times$ speedup on FLUX, 5.56$\times$ speedup on HunyuanVideo, 6.24$\times$ speedup on Qwen-Image and Qwen-Image-Edit without retraining.

Deep Learning · Generative Models and Autoencoders

Wei Pan, Huiguo He, Hiuyi Cheng, Yilin Shi, Lianwen Jin

Deep generative models have advanced text-to-online handwriting generation (TOHG), which aims to synthesize realistic pen trajectories conditioned on textual input and style references. However, most existing methods still primarily focus on character- or word-level generation, resulting in inefficiency and a lack of holistic structural modeling when applied to full text lines. To address these issues, we propose DiffInk, the first latent diffusion Transformer framework for full-line handwriting generation. We first introduce InkVAE, a novel sequential variational autoencoder enhanced with two complementary latent-space regularization losses: (1) an OCR-based loss enforcing glyph-level accuracy, and (2) a style-classification loss preserving writing style. This dual regularization yields a semantically structured latent space where character content and writer styles are effectively disentangled. We then introduce InkDiT, a novel latent diffusion Transformer that integrates target text and reference styles to generate coherent pen trajectories. Experimental results demonstrate that DiffInk outperforms existing state-of-the-art (SOTA) methods in both glyph accuracy and style fidelity, while significantly improving generation efficiency.

Deep Learning · Generative Models and Autoencoders

Bowei Chen, Sai Bi, Hao Tan, HE Zhang, Tianyuan Zhang, Zhengqi Li, Yuanjun Xiong, Jianming Zhang, Kai Zhang

In this work, we propose aligning pretrained visual encoders to serve as tokenizers for latent diffusion models in image generation. Unlike training a variational autoencoder (VAE) from scratch, which primarily emphasizes low-level details, our approach leverages the rich semantic structure of foundation encoders. We introduce a three-stage alignment strategy called AlignTok: (1) freeze the encoder and train an adapter and a decoder to establish a semantic latent space; (2) jointly optimize all components with an additional semantic preservation loss, enabling the encoder to capture perceptual details while retaining high-level semantics; and (3) refine the decoder for improved reconstruction quality. This alignment yields semantically rich image tokenizers that benefit diffusion models. On ImageNet 256$\times$256, our tokenizer accelerates the convergence of diffusion models, reaching a gFID of 1.90 within just 64 epochs, and improves generation both with and without classifier-free guidance. Scaling to LAION, text-to-image models trained with our tokenizer consistently outperforms FLUX VAE and VA-VAE under the same training steps. Overall, our method is simple, scalable, and establishes a semantically grounded paradigm for continuous tokenizer design.

Deep Learning · Generative Models and Autoencoders

Harry Dong, David Brandfonbrener, Eryk Helenowski, Yun He, Mrinal Kumar, Han Fang, Yuejie Chi, Karthik Abinav Sankararaman

Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8\%-5.1\%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 39\% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

Deep Learning · Generative Models and Autoencoders

Longze Chen, Lu Wang, Renke Shan, Ze Gong, Run Luo, Jiaming Li, Jing Luo, Qiyao Wang, Min Yang

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically demand costly point-wise supervision, while DRMs produce uncalibrated relative scores that lack probabilistic interpretation. To address these challenges, we introduce a novel reward modeling paradigm: Probabilistic Reward Model (PRM). Instead of modeling reward as a deterministic scalar, our approach treats it as a random variable, learning a full probability distribution for the quality of each response. To make this paradigm practical, we present its closed-form, discrete realization: the **Ordinal Probabilistic Reward Model** (OPRM), which discretizes the quality score into a finite set of ordinal ratings. Building on OPRM, we propose a data-efficient training strategy called **Region Flooding Tuning** (RgFT). It enables rewards to better reflect absolute text quality by incorporating quality-level annotations, which guide the model to concentrate the probability mass within corresponding rating sub-regions. Experiments on various reward model benchmarks show that our method improves accuracy by **2.9% ～ 7.4%** compared to prior reward models, demonstrating strong performance and data efficiency. Analysis of the score distribution provides evidence that our method captures not only relative rankings but also absolute quality.

Deep Learning · Generative Models and Autoencoders

Soochul Park, Yeon Ju Lee

Diffusion models achieve state-of-the-art image quality. However, sampling is costly at inference time because it requires a large number of function evaluations (NFEs). To reduce NFEs, classical ODE numerical methods have been adopted. Yet, the choice of prediction type and integration domain leads to different sampling behaviors. To address these issues, we introduce Dual-Solver, which generalizes multistep samplers through learnable parameters that continuously (i) interpolate among prediction types, (ii) select the integration domain, and (iii) adjust the residual terms. It retains the standard predictor-corrector structure while preserving second-order local accuracy. These parameters are learned via a classification-based objective using a frozen pretrained classifier (e.g., MobileNet or CLIP). For ImageNet class-conditional generation (DiT, GM-DiT) and text-to-image generation (SANA, PixArt-$\alpha$), Dual-Solver improves FID and CLIP scores in the low-NFE regime ($3 \le$ NFE $\le 9$) across backbones.

Deep Learning · Generative Models and Autoencoders

Nuria Chandra, Yucen Li, Alan Amin, Alex Ali, Joshua Rollins, Sebastian W. Ober, Aniruddh Raghu, Andrew Gordon Wilson

To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite their shared goal, these models have disparate algorithms, theoretical structures, and tradeoffs: discrete diffusion has the most natural domain, Gaussian diffusion has more mature algorithms, and diffusion on the simplex in principle combines the strengths of the other two but in practice suffers from a numerically unstable stochastic processes. Ideally we could see each of these models as instances of the same underlying framework, and enable practitioners to switch between models for downstream applications. However previous theories have only considered connections in special cases. Here we build a theory unifying all three methods of discrete diffusion as different parameterizations of the same underlying process: the Wright-Fisher population genetics model. In particular, we find simplicial and Gaussian diffusion as two large-population limits. Our theory formally connects the likelihoods and hyperparameters of these models and leverages decades of mathematical genetics literature to unlock stable simplicial diffusion. Finally, we relieve the practitioner of balancing model trade-offs by demonstrating it is possible to train a single model that can perform diffusion in any of these three domains at test time. Our experiments show that Wright-Fisher simplicial diffusion is more stable and outperforms previous simplicial diffusion models on conditional DNA generation. We also show that we can train models on multiple domains at once that are competitive with models trained on any individual domain.

Deep Learning · Generative Models and Autoencoders

Yunhan Yang, Yuanchen Guo, Yukun Huang, Zi-Xin Zou, Zhipeng Yu, Yangguang Li, Yanpei Cao, Xihui Liu

3D part amodal segmentation--decomposing a 3D shape into complete, semantically meaningful parts, even when occluded--is a challenging but crucial task for 3D content creation and understanding. Existing 3D part segmentation methods only identify visible surface patches, limiting their utility. Inspired by 2D amodal segmentation, we introduce this novel task to the 3D domain and propose a practical, two-stage approach, addressing the key challenges of inferring occluded 3D geometry, maintaining global shape consistency, and handling diverse shapes with limited training data. First, we leverage existing 3D part segmentation to obtain initial, incomplete part segments. Second, we introduce HoloPart, a novel diffusion-based model, to complete these segments into full 3D parts. HoloPart utilizes a specialized architecture with local attention to capture fine-grained part geometry and global shape context attention to ensure overall shape consistency. We introduce new benchmarks based on the ABO and PartObjaverse-Tiny datasets and demonstrate that HoloPart significantly outperforms state-of-the-art shape completion methods. By incorporating HoloPart with existing segmentation techniques, we achieve promising results on 3D part amodal segmentation, opening new avenues for applications in geometry editing, animation, and material assignment.

Deep Learning · Generative Models and Autoencoders

Alireza Mousavi-Hosseini, Stephen Zhang, Michal Klein, marco cuturi

Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(x_0,x_1)$ and ensuring that the velocity field is aligned, on average, with $x_1-x_0$ when evaluated along a time-indexed segment linking $x_0$ to $x_1$. While these noise/data pairs are sampled independently by default, they can also be selected more carefully by matching batches of $n$ noise to $n$ target points using an optimal transport (OT) solver. Although promising in theory, the OT flow matching (OT-FM) approach (Pooladian et al., 2023, Tong et al., 2024) is not widely used in practice. Zhang et al. (2025), pointed out recently that OT-FM truly starts paying off when the batch size $n$ grows significantly, which only a multi-GPU implementation of the Sinkhorn algorithm can handle. Unfortunately, the pre-compute costs of running Sinkhorn can quickly balloon, requiring $O(n^2/\varepsilon^2)$ operations for every $n$ pairs used to fit the velocity field, where $\varepsilon$ is a regularization parameter that should be typically small to yield better results. To fulfill the theoretical promises of OT-FM, we propose to move away from batch-OT and rely instead on a semidiscrete formulation that can leverage the fact that the target dataset distribution is usually of finite size $N$. The SD-OT problem is solved by estimating a dual potential vector of size $N$ using SGD; using that vector, freshly sampled noise vectors at train time can then be matched with data points at the cost of a maximum inner product search (MIPS) over the dataset. Semidiscrete FM (SD-FM) removes the quadratic dependency on $n/\varepsilon$ that bottlenecks OT-FM. SD-FM beats both FM and OT-FM on all training metrics and inference budget constraints, across multiple datasets, on unconditional/conditional generation, or when using mean-flow models.

Deep Learning · Generative Models and Autoencoders

Elias Chaibub Neto

Synthetic data generation for tabular datasets is shifting toward the use of large, general-purpose foundation models. TabPFN, a state-of-the-art example, uses in-context learning to generate probabilistic predictions conditioned on observed examples in a single forward pass. However, when variables are only weakly associated with others, the model's ability to generate realistic synthetic data deteriorates, as the context examples provide little predictive signal. To address this, we introduce the maximal information auxiliary variable (MIAV) strategy, which increases context information with auxiliary variables constructed by rank-matching random noise variables to real data. We establish theoretical properties of the approach which explain its good performance for weakly associated variables. Additional practical advantages of the MIAV approach include improved computational efficiency and invariance to variable order during the synthetic data generation process. Empirical evaluations, on simulated and real datasets, illustrate how the MIAV strategy improves data generation when compared to direct application of TabPFN, and is competitive against other baselines. To illustrate the generality of the MIAV approach we also present an implementation based on the TabICL model (a more scalable tabular foundation model restricted to classification tasks) for performing synthetic data generation on categorical datasets. Overall, MIAV offers an effective foundation model–based alternative to bespoke synthetic data generators.

Reinforcement Learning · Deep RL

Baptiste Debes, Tinne Tuytelaars

Gradient-regularized value learning methods improve sample efficiency by leveraging learned models of transition dynamics and rewards to estimate return gradients. However, existing approaches, such as MAGE, struggle in stochastic or noisy environments, limiting their applicability. In this work, we address these limitations by extending distributional reinforcement learning on continuous state-action spaces to model not only the distribution over scalar state-action value functions but also over their gradients. We refer to this approach as Distributional Sobolev Training. Inspired by Stochastic Value Gradients (SVG), our method utilizes a one-step world model of reward and transition distributions implemented via a conditional Variational Autoencoder (cVAE). The proposed framework is sample-based and employs Max-sliced Maximum Mean Discrepancy (MSMMD) to instantiate the distributional Bellman operator. We prove that the Sobolev-augmented Bellman operator is a contraction with a unique fixed point, and highlight a fundamental smoothness trade-off underlying contraction in gradient-aware RL. To validate our method, we first showcase its effectiveness on a simple stochastic reinforcement‐learning toy problem, then benchmark its performance on several MuJoCo environments.

Deep Learning · Generative Models and Autoencoders

Bolin Zhao, Xiaoyu Zhang, Yuting Dong, Xin Lu, Wei Lin, Qunxi Zhu

Flow matching (FM) based on Ordinary Differential Equations (ODEs) has achieved significant success in generative tasks. However, it faces several inherent limitations, including an inability to model trajectory intersections, capture delay dynamics, and handle transfer between heterogeneous distributions. These limitations often result in a significant mismatch between the modeled transfer process and real-world phenomena, particularly when key coupling or inherent structural information between distributions must be preserved. To address these issues, we propose Delay Flow Matching (DFM), a new FM framework based on Delay Differential Equations (DDEs). Theoretically, we show that DFM possesses universal approximation capability for continuous transfer maps. By incorporating delay terms into the vector field, DFM enables trajectory intersections and better captures delay dynamics. Moreover, by designing appropriate initial functions, DFM ensures accurate transfer between heterogeneous distributions. Consequently, our framework preserves essential coupling relationships and achieves more flexible distribution transfer strategies. We validate DFM's effectiveness across synthetic datasets, single-cell data, and image-generation tasks.

Deep Learning · Generative Models and Autoencoders

Chunyang Jiang, Yonggang Zhang, Yiyang Cai, Chi-Min Chan, Yulong Liu, Mingming Chen, Wei Xue, Yike Guo

The rising cost of acquiring supervised data has driven significant interest in self-improvement for large language models (LLMs). Straightforward unsupervised signals like majority voting have proven effective in generating pseudo-labels for verifiable tasks, while their applicability to unverifiable tasks (e.g., translation) is limited by the open-ended character of responses. As a result, self-evaluation mechanisms (e.g., self-judging and entropy minimization) are predominantly used to derive pseudo-labels. However, self-evaluation relying on LLMs typically incurs high computational overhead and introduces overconfidence issues due to intrinsic biases. To address these challenges, we propose a novel self-evaluation-free approach for unverifiable tasks, designed for lightweight yet effective self-improvement. Inspired by majority voting commonly employed in verifiable tasks, we propose semantic voting as a novel mechanism that relaxes the principle of hard matching (i.e., exact matching) toward soft matching (i.e., semantic similarity). Soft matching is achieved by leveraging a lightweight sentence embedding model to quantify semantic similarity, thereby mitigating excessive computational burden and intrinsic bias-associated limitations of self-evaluation. Comprehensive experiments demonstrate that our method achieves substantial gains in computational efficiency and overall better performance than self-evaluation methods across diverse model architectures and tasks.

Deep Learning · Generative Models and Autoencoders

Cristian Jensen, Luca Schaufelberger, Riccardo De Santi, Kjell Jorner, Andreas Krause

Adapting large-scale flow and diffusion models to downstream tasks through reward optimization is essential for their adoption in real-world applications, including scientific discovery and image generation. While recent fine-tuning methods based on reinforcement learning and stochastic optimal control achieve compelling performance, they face severe scalability challenges due to high memory demands that scale with model complexity. In contrast, methods that disentangle reward adaptation from base model complexity, such as Classifier Guidance (CG), offer flexible control over computational resource requirements. However, CG suffers from limited reward expressivity and a train-test distribution mismatch due to its offline nature. To overcome the limitations of fine-tuning methods and CG, we propose Value Matching (VM), an online algorithm for learning the value function within an optimal control setting. VM provides tunable memory and compute demands through flexible value network complexity, supports optimization of non-differentiable rewards, and operates on-policy, which enables going beyond the data distribution to discover high-reward regions. Experimentally, we evaluate VM across image generation and molecular design tasks. We demonstrate improved stability and sample efficiency over CG and achieve comparable performance to fine-tuning approaches while requiring less than 5% of their memory usage.

Qian Li, Yuxiao Hu, Juncheng Liu, Yuntian Chen

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space–based SR framework following the "map construction $\rightarrow$ coarse localization $\rightarrow$ fine search" paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured "map" of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the candidate region, leveraging smooth latent gradients. From a Bayesian perspective, GenSR reframes SR task as maximizing the conditional distribution $p({\rm Equ.}|{\rm Num.})$, with CVAE training achieving this objective through the Evidence Lower Bound (ELBO). This new perspective provides a theoretical guarantee for the effectiveness of GenSR. Extensive experiments show that GenSR jointly optimizes predictive accuracy, expression simplicity, and computational efficiency, while remaining robust under noise.

Deep Learning · Generative Models and Autoencoders

Tao Zhang, Jia-Shu Pan, Ruiqi Feng, Tailin Wu

Inspired by human SYSTEM 2 thinking, LLMs excel at complex reasoning tasks via extended Chain-of-Thought. However, similar test-time scaling for diffusion models to tackle complex reasoning remains largely unexplored. From existing work, two primary challenges emerge in this setting: (i) the dependence on an external verifier indicating a notable gap from intrinsic reasoning of human intelligence without any external feedback, and (ii) the lack of an efficient search algorithm. In this paper, we introduce the Verifier-free Test-time Scalable Diffusion Model (VFScale) to achieve scalable intrinsic reasoning, which equips number-of-sample test-time scaling with the intrinsic energy function of diffusion models as the verifier. Concretely, VFScale comprises two key innovations to address the aforementioned challenges. On the training side, VFScale consists of a novel MRNCL loss and a KL regularization to improve the energy landscape, ensuring that the learned energy function itself serves as a reliable verifier. On the inference side, VFScale integrates the denoising process with a novel hybrid Monte Carlo Tree Search (hMCTS) to improve search efficiency. On challenging reasoning tasks of Maze and Sudoku, we demonstrate the effectiveness of VFScale's training objective and scalable inference method. In particular, trained with Maze sizes of up to 6×6, our VFScale solves 88\% of Maze problems with much larger sizes of 15×15, while standard diffusion model completely fails. The code can be found at https://github.com/AI4Science-WestlakeU/VFScale.

Deep Learning · Generative Models and Autoencoders

Mehul Damani, Isha Puri, Stewart Slocum, Idan Shenfeld, Leshem Choshen, Yoon Kim, Jacob Andreas

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language “reasoning chains”, their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or “hallucinate”) in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score—a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations—outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Deep Learning · Generative Models and Autoencoders

Sattwik Basu, Chaitanya Amballa, Zhongweiyang Xu, Jorge Vančo Sampedro, Srihari Nelakuditi, Romit Roy Choudhury

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward operators introduce a distinct set of challenges. As a concrete instance, we consider the problem of reconstructing spatial layouts, such as floorplans, from human movement trajectories, where the underlying path-generation process is inherently non-differentiable and only partially known. In such problems, direct likelihood-based guidance becomes unstable, since the underlying path-planning process does not provide reliable gradients. We break-away from existing diffusion-based posterior samplers and reformulate likelihood-based guidance in a smoother embedding space. This embedding space is learned using a contrastive objective to bring compatible trajectory-floorplan pairs close together while pushing mismatched pairs apart. We show that this surrogate likelihood score in the embedding space provides a valid approximation to the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent reconstructions and is more robust than existing inverse-solvers and guided diffusion. Beyond spatial mapping, we show that our method can be applied more broadly, suggesting a route toward solving generalized blind inverse problems using diffusion models.

Deep Learning · Generative Models and Autoencoders

Yuxin Liu, Kaiming Wang, Chenguang Yang, Yulia Gel, Yuzhou Chen

Spatio-temporal point process (STPP) data appear in many domains. A natural way to model them is to describe how the instantaneous event rate varies over space and time given the observed history which enables interpretation, interaction detection, and forecasting. Traditional parametric kernel-based models, while historically dominant, struggle to capture complex nonlinear patterns. In contrast, deep learning methods leverage the representational power of neural networks to aggregate historical events and integrate spatio-temporal point processes. However, existing deep learning methods often process space and time independently, overlooking the spatio-temporal dependencies. To address this limitation, we propose a novel method called Topology-ENhanced Diffusion Model (TEN-DM), including two key components namely spatio-temporal graph construction and multimodal topological feature representation learning. Further, we use temporal query technique to effectively capture periodic temporal patterns for learning effective temporal representations. Extensive experiments show the effectiveness of TEN-DM on multiple STPP datasets compared to state-of-the-art methods.

Applications · Time Series

Kun Liu, Renjun Jia, Ruifeng Yang, Xirui Zeng, Yuqi Liang, Cen Chen

Effectively modeling cross-variate dependencies is a central, yet challenging, task in multivariate time series forecasting. While attention-based methods have advanced the state-of-the-art by capturing global cross-variate dependencies, their quadratic complexity with respect to the number of variates severely limits their scalability. In this work, we challenge the necessity of global dependency modeling. We posit, through both theoretical analysis and empirical evidence, that modeling local cross-variate interactions is not only sufficient but also more efficient for many dense dependency systems. Motivated by this core insight, we propose VPNet, a novel architecture that excels in both accuracy and efficiency. VPNet's design is founded on two key principles: a channelized reinterpretation of patch embeddings into a higher-level variate-patch field, and a specialized VarTCNBlock that operates upon it. Specifically, the model first employs a patch-level autoencoder to extract robust local representations. In a pivotal step, these representations are then re-conceptualized as a 2D field constructed over a "variates × patches" grid. The VarTCNBlock then applies depthwise 2D convolutions across this field to efficiently capture local spatio-temporal patterns (i.e., cross-variate and temporal dependencies simultaneously), followed by pointwise convolutions for feature mixing. This design ensures that the computational complexity scales linearly with the number of variates. Finally, variate-wise prediction heads map the refined historical patch representations to future ones, which are decoded back into the time domain. Extensive experiments demonstrate that VPNet not only achieves state-of-the-art performance across multiple benchmarks but also offers significant efficiency gains, establishing it as a superior and scalable solution for high-dimensional forecasting.