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Computer Vision · Vision Models & Multimodal

Yueming Xu, Jiahui Zhang, Ze Huang, Yurui Chen, Yanpeng Zhou, Dave Chen, Yu-Jie Yuan, Pengxiang Xia, Guowei Huang, Xinyue Cai 等

Despite the impressive progress on understanding and generating images shown by the recent unified architectures, the integration of 3D tasks remains challenging and largely unexplored. In this paper, we introduce UniUGG, the first unified understanding and generation framework for 3D modalities. Our unified framework employs an LLM to comprehend and decode sentences and 3D representations. At its core, we propose a spatial decoder leveraging a latent diffusion model to generate high-quality 3D representations. This allows for the generation and imagination of 3D scenes based on a reference image and an arbitrary view transformation, while remaining supports for spatial visual question answering (VQA) tasks. Additionally, we propose a geometric-semantic learning strategy to pretrain the vision encoder. This design jointly captures the input's semantic and geometric cues, enhancing both spatial understanding and generation. Extensive experimental results demonstrate the superiority of our method in visual representation, spatial understanding, and 3D generation.

Alexi Gladstone, Ganesh Nanduru, Md Mofijul Islam, Peixuan Han, Hyeonjeong Ha, Aman Chadha, Yilun Du, Heng Ji, Jundong Li, Tariq Iqbal

Inference-time computation, analogous to human System 2 Thinking, has recently become popular for improving model performance. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question “Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?” We find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs)---a new class of Energy-Based Models (EBMs)---to assign an energy value to every input and candidate-prediction, enabling predictions through energy minimization until convergence. To support this approach, we introduce several key techniques for stable and parallelizable training, which enable the emergence of strong System 2 Thinking capabilities and scalable EBMs. Across discrete and continuous modalities, we find EBTs outperform the Transformer++ approach, scaling up to 35% faster during pretraining, and improving inference-time performance by up to 29%. EBTs also surpass Diffusion Transformers on image denoising while requiring 99% fewer forward passes. Moreover, System 2 Thinking with EBTs yields larger performance gains on data that is farther out-of-distribution, and EBTs achieve better results than existing models on most downstream tasks despite achieving the same or worse pretraining performance, enabling EBTs to generalize better than existing approaches. Consequently, EBTs are a flexible and exciting new approach for scaling both the learning and thinking capabilities of models.

Deep Learning · Generative Models and Autoencoders

Alexi Gladstone, Ganesh Nanduru, Md Mofijul Islam, Peixuan Han, Hyeonjeong Ha, Aman Chadha, Yilun Du, Heng Ji, Jundong Li, Tariq Iqbal

Inference-time computation, analogous to human System 2 Thinking, has recently become popular for improving model performance. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question “Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?” We find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs)---a new class of Energy-Based Models (EBMs)---to assign an energy value to every input and candidate-prediction, enabling predictions through energy minimization until convergence. To support this approach, we introduce several key techniques for stable and parallelizable training, which enable the emergence of strong System 2 Thinking capabilities and scalable EBMs. Across discrete and continuous modalities, we find EBTs outperform the Transformer++ approach, scaling up to 35% faster during pretraining, and improving inference-time performance by up to 29%. EBTs also surpass Diffusion Transformers on image denoising while requiring 99% fewer forward passes. Moreover, System 2 Thinking with EBTs yields larger performance gains on data that is farther out-of-distribution, and EBTs achieve better results than existing models on most downstream tasks despite achieving the same or worse pretraining performance, enabling EBTs to generalize better than existing approaches. Consequently, EBTs are a flexible and exciting new approach for scaling both the learning and thinking capabilities of models.

General Machine Learning · Everything Else

Liu Peng, Yaochu Jin

This paper investigates a critical challenge in modern machine learning: how different probabilistic models withstand low-quality training data. Through a systematic, comparative investigation, we reveal a stark spectrum of robustness. Empirically, we find that autoregressive language models exhibit remarkable resilience against both token-level noise and structural corruption (for GPT-2, test NLL increases modestly from 2.87 to 3.59 despite 50\% corruption). By sharp contrast, class-conditional diffusion models degrade catastrophically under identical noise levels (image-label consistency plummets by 56.81\%), while image classifiers show a moderate vulnerability that diminishes with dataset scale. To explain these discrepancies, we analyze the results through a multi-perspective lens integrating information theory, PAC learning, and gradient dynamics. This framework identifies what informational properties drive robustness, why they are required for generalization, and how the optimization process achieves this resilience. These analyses suggest that robustness is heavily influenced by two key principles: the richness of conditioning information, which constrains the learning problem, and the absolute information content of the training data, which allows the signal from correct information to dominate statistical noise.

Deep Learning · Everything Else

Sahil Kumar, Namrataben Patel, Honggang Wang, Youshan Zhang

MambaVoiceCloning (MVC) asks whether the conditioning path of diffusion-based TTS can be made fully SSM-only at inference—removing all attention and explicit RNN-style recurrence layers across text, rhythm, and prosody—while preserving or improving quality under controlled conditions. MVC combines a gated bidirectional Mamba text encoder, a Temporal Bi-Mamba supervised by a lightweight alignment teacher discarded after training, and an Expressive Mamba with AdaLN modulation, yielding linear-time $\mathcal{O}(T)$ conditioning with bounded activation memory and practical finite look-ahead streaming. Unlike prior Mamba--TTS systems that remain hybrid at inference, MVC removes attention-based duration and style modules under a fixed StyleTTS2 mel--diffusion--vocoder backbone. Trained on LJSpeech/LibriTTS and evaluated on VCTK, CSS10 (ES/DE/FR), and long-form Gutenberg passages, MVC achieves modest but statistically reliable gains over StyleTTS2, VITS, and Mamba--attention hybrids in MOS/CMOS, F$_0$ RMSE, MCD, and WER, while reducing encoder parameters to 21M and improving throughput by $1.6\times$. Diffusion remains the dominant latency source, but SSM-only conditioning improves memory footprint, stability, and deployability. Code available at: \url{https://github.com/sahilkumar15/MVC}.

Deep Learning · Generative Models and Autoencoders

Zeqi Ye, Qijie Zhu, Molei Tao, Minshuo Chen

Diffusion models have achieved remarkable success across diverse domains, but they remain vulnerable to memorization---reproducing training data rather than generating novel outputs. This not only limits their creative potential but also raises concerns about privacy and safety. While empirical studies have explored mitigation strategies, theoretical understanding of memorization remains limited. We address this gap through developing a dual-separation result via two complementary perspectives: statistical estimation and network approximation. From the estimation side, we show that the ground-truth score function does not minimize the empirical denoising loss, creating a separation that drives memorization. From the approximation side, we prove that implementing the empirical score function requires network size to scale with sample size, spelling a separation compared to the more compact network representation of the ground-truth score function. Guided by these insights, we develop a pruning-based method that reduces memorization while maintaining generation quality in diffusion transformers.

Applications · Time Series

Xiaoda Wang, Kaiqiao Han, Yuhao Xu, Xiao Luo, Yizhou Sun, Wei Wang, Carl Yang

Cardiovascular disease (CVD) is a leading cause of mortality worldwide. Electrocardiograms (ECGs) are the most widely used non-invasive tool for cardiac assessment, yet large, well-annotated ECG corpora are scarce due to cost, privacy, and workflow constraints. Generating ECGs can aid mechanistic understanding of cardiac electrical activity, enable the construction of large, heterogeneous, and unbiased datasets, and facilitate privacy-preserving data sharing. Generating realistic ECG signals from clinical context is important yet underexplored. Recent work has leveraged diffusion models for text-to-ECG generation, but two challenges remain: (i) existing methods often overlook physiological simulator knowledge of cardiac activity; and (ii) they ignore broader, experience-based clinical knowledge grounded in real-world practice. To address these gaps, we propose **SE-Diff**, a physiological simulator- and experience-enhanced diffusion model for comprehensive ECG generation. SE-Diff integrates a lightweight ordinary differential equation (ODE)–based ECG simulator into the diffusion process via a beat decoder and simulator-consistent constraints, injecting mechanistic priors that promote physiologically plausible waveforms. In parallel, we design an LLM-powered, experience retrieval–augmented strategy to inject clinical knowledge, providing stronger guidance for ECG generation. Extensive experiments on real-world ECG datasets demonstrate that SE-Diff improves both signal fidelity and text–ECG semantic alignment over baselines. We further show that simulator-based and experience-based knowledge benefit downstream ECG classification.

Theory · Learning Theory

Xingyu Xu, Ziyi Zhang, Yorie Nakahira, Guannan Qu, Yuejie Chi

Diffusion generative models have demonstrated remarkable empirical success in the recent years and are now considered the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data distribution to a noise distribution spanning the whole space, and a backward process, which inverts this transformation to recover the data distribution from noise. Most of the existing literature assumes that the underlying space is Euclidean. However, in many practical applications, the data are constrained to lie on a submanifold of Euclidean space. Addressing this setting, de Bortoli et al. (2022) introduced Riemannian diffusion models and proved that using an exponentially small step size yields small sampling error in Wasserstein distance, provided the data distribution is smooth and strictly positive. In this paper, we prove that a *polynomially small stepsize* suffices to guarantee small sampling error in total variation distance, without any assumption on the smoothness or positivity of the data distribution. Our analysis only requires mild and standard curvature assumptions on the underlying manifold. The main ingredients in our proof are Li-Yau estimate for log-gradient of heat kernel, and Minakshisundaram-Pleijel parametrix expansion for perturbed heat equation. Our approach opens the door to a sharper analysis of diffusion models on non-Euclidean spaces.

Computer Vision · Image and Video Generation

Jiaxing Cui, Jie Wu, Ming Li, Tao Yang, Xiaojie Li, Rui Wang, Andrew Bai, Yuanhao Ban, Cho-Jui Hsieh

Diffusion models have revolutionized image and video generation, achieving unprecedented visual quality. However, their reliance on transformer architectures incurs prohibitively high computational costs, particularly when extending generation to long videos. Recent work has explored autoregressive formulations for long video generation, typically by distilling from short-horizon bidirectional teachers. Nevertheless, given that teacher models cannot synthesize long videos, the extrapolation of student models beyond their training horizon often leads to pronounced quality degradation, arising from the compounding of errors within the continuous latent space. In this paper, we propose a simple yet effective approach to mitigate quality degradation in long-horizon video generation without requiring supervision from long-video teachers or retraining on long video datasets. Our approach centers on exploiting the rich knowledge of teacher models to provide guidance for the student model through sampled segments drawn from self-generated long videos. Our method maintains temporal consistency while scaling video length by up to 20$\times$ beyond teacher's capability, avoiding common issues such as over-exposure and error-accumuation without recomputing overlapping frames like previous methods. When scaling up the computation, our method shows the capability of generating videos up to 4 minutes and 15 seconds, equivalent to 99.9\% of the maximum span supported by our base model’s position embedding and more than 50x longer than that of our baseline model. Experiments on standard benchmarks and our proposed improved benchmark demonstrate that our approach substantially outperforms baseline methods in both fidelity and consistency. Our long-horizon videos demo can be found at http://self-forcing-plus-plus.github.io/

Deep Learning · Generative Models and Autoencoders

Tianze Luo, Haotian Yuan, Zhuang Liu

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

Deep Learning · Generative Models and Autoencoders

BumJun Kim, Dongjae Jeon, Dueun Kim, Wonje Jeung, Albert No

Diffusion large language models (dLLMs) have emerged as a promising alternative to autoregressive models, offering flexible generation orders and strong performance on complex reasoning tasks. However, instruction-tuned dLLMs exhibit a critical vulnerability we term \ overflow: as allocated sequence length increases, responses paradoxically become shorter, collapsing into early termination or degenerating into streams of \ tokens. Although noticed in practice, this issue has not been systematically analyzed. We trace its root cause to the dual role of \ as both termination and padding, which concentrates probability mass on \ at later positions and propagates backward to trigger early termination. To address this, we introduce Rainbow Padding, a simple remedy that replaces repeated \ placeholders with a repeating cycle of distinct padding tokens, distributing probability mass and breaking \ dominance. Experiments show that Rainbow Padding substantially improves length robustness and output quality, with as few as seven padding tokens to prevent early termination. Moreover, the method integrates efficiently into existing instruction-tuned models: LoRA fine-tuning for a single epoch on minimal data yields significant improvements, making this solution highly practical. The project is available at ~\url{https://ai-isl.github.io/rainbow-padding}

Applications · Everything Else

Teng Tu, Ai Li, Yunshan Ma, Shuo Xu, Xiaohao Liu, Haokai Ma, Liang Pang, Tat-Seng Chua

As a central task in product bundling, bundle construction aims to select a subset of items from large item catalogs to build an entire bundle or, more practically, complete a partial bundle. Existing methods often rely on the sequential construction paradigm that predicts items one at a time, nevertheless, this paradigm is fundamentally unsuitable for the essentially unordered bundles. In contrast, non-sequential methods model a bundle as a set, but still face two dimensionality curses: the combinatorial space grows exponentially with both bundle length and catalog size. Accordingly, we identify two technical challenges: 1) how to effectively and efficiently model the higher-order intra-bundle relations with the growth of bundle length; and 2) how to learn item representations that remain discriminative while avoiding search directly over a huge item catalog. To address these challenges, we propose DDBC, a Discrete Diffusion model for Bundle Construction. DDBC leverages a masked denoising diffusion process to build bundles non-sequentially, capturing joint dependencies among items without relying on a fixed decoding order, thereby partially alleviating the combinatorial challenge introduced by increasing bundle length. To mitigate the curse of large catalog size, we integrate residual vector quantization (RVQ), which compresses item embeddings into discrete codes drawn from a globally shared codebook, enabling more efficient search while retaining semantic granularity. We evaluate our method on real-world bundle construction datasets of music playlist continuation and fashion outfit completion, and the experimental results show that DDBC can achieve more than 100\% relative performance improvements compared with state-of-the-art baseline methods. Ablation and model analyses further confirm the effectiveness of both the diffusion backbone and the RVQ tokenizer, with gains becoming more pronounced for longer bundles and larger catalogs. Our code is available at https://github.com/241416/DDBC.

Computer Vision · Image and Video Generation

Yuan Wang, Yuhao Wan, Siming Zheng, Bo Li, Qibin Hou, Peng-Tao Jiang

Recent works have explored reference-based super-resolution (RefSR) to mitigate hallucinations in diffusion-based image restoration. A key challenge is that real-world degradations make correspondences between low-quality (LQ) inputs and reference (Ref) images unreliable, requiring adaptive control of reference usage. Existing methods either ignore LQ–Ref correlations or rely on brittle explicit matching, leading to over-reliance on misleading references or under-utilization of valuable cues. To address this, we propose Ada-RefSR, a single-step diffusion framework guided by a "Trust but Verify " principle: reference information is leveraged when reliable and suppressed otherwise. Its core component, Adaptive Implicit Correlation Gating (AICG), employs learnable summary tokens to distill dominant reference patterns and capture implicit correlations with LQ features. Integrated into the attention backbone, AICG provides lightweight, adaptive regulation of reference guidance, serving as a built-in safeguard against erroneous fusion. Experiments on multiple datasets demonstrate that Ada-RefSR achieves a strong balance of fidelity, naturalness, and efficiency, while remaining robust under varying reference alignment. Code and models are available at https://github.com/vivoCameraResearch/AdaRefSR.

Computer Vision · Image and Video Generation

Yang Yang, Siming Zheng, Qirui Yang, Jinwei Chen, Boxi Wu, Xiaofei He, Deng Cai, Bo Li, Peng-Tao Jiang

Diffusion models have recently emerged as powerful tools for camera simulation, enabling both geometric transformations and realistic optical effects. Among these, image-based bokeh rendering has shown promising results, but diffusion for video bokeh remains unexplored. Existing image-based methods are plagued by temporal flickering and inconsistent blur transitions, while current video editing methods lack explicit control over the focus plane and bokeh intensity. These issues limit their applicability for controllable video bokeh. In this work, we propose a one-step diffusion framework for generating temporally coherent, depth-aware video bokeh rendering. The framework employs a multi-plane image (MPI) representation adapted to the focal plane to condition the video diffusion model, thereby enabling it to exploit strong 3D priors from pretrained backbones. To further enhance temporal stability, depth robustness, and detail preservation, we introduce a progressive training strategy. Experiments on synthetic and real-world benchmarks demonstrate superior temporal coherence, spatial accuracy, and controllability, outperforming prior baselines. This work represents the first dedicated diffusion framework for video bokeh generation, establishing a new baseline for temporally coherent and controllable depth-of-field effects. Project page is available at this website https://vivocameraresearch.github.io/any2bokeh/.

Deep Learning · Generative Models and Autoencoders

Zeqing Wang, Gongfan Fang, Xinyin Ma, Xingyi Yang, Xinchao Wang

While diffusion language models (DLMs) offer a promising alternative to autoregressive models (ARs), existing open-source DLMs suffer from high inference latency. This bottleneck is mainly due to the attention’s quadratic complexity with respect to context length in computing all query–key pairs. Intuitively, to reduce this complexity, a natural strategy is to restrict attention to sparse patterns that retain only the most relevant connections. Such approaches are well-established in ARs, where attention follows fixed and clearly defined sparse patterns. However, in DLMs, we observe distinct sparsity behaviors: (1) attention patterns vary across heads, (2) attention patterns in each head remain highly similar across denoising steps, and (3) early denoising steps are critical for generation. These findings render sparse attention methods designed for ARs largely incompatible with DLMs, as they fail to capture head-specific structures and risk degrading generation when applied in early denoising steps. To address these challenges, we propose **SparseD**, a novel sparse attention method for DLMs. Leveraging the observations, SparseD only requires pre-computing head-specific sparse patterns one time, and reuses them across all steps. This prevents recomputing sparse patterns at each denoising step. Meanwhile, SparseD uses full attention in the early steps, then switches to sparse attention later to maintain generation quality. Together, these establish SparseD as a practical and efficient solution for deploying DLMs in long-context applications. Experimental results demonstrate that SparseD achieves lossless acceleration, delivering up to $1.50\times$ speedup over FlashAttention at a 64k context length with 1,024 denoising steps. Code is available at https://github.com/INV-WZQ/SparseD.

Deep Learning · Generative Models and Autoencoders

Shirin Shoushtari, Yi Wang, Xiao Shi, Salman Asif, Ulugbek Kamilov

Out-of-distribution (OOD) detection is critical for the safe deployment of machine learning systems in safety-sensitive domains. Diffusion models have recently emerged as powerful generative models, capable of capturing complex data distributions through iterative denoising. Building on this progress, recent work has explored their potential for OOD detection. We propose *EigenScore*, a new OOD detection method that leverages the eigenvalue spectrum of the posterior covariance induced by a diffusion model. We argue that posterior covariance provides a consistent signal of distribution shift, leading to larger trace and leading eigenvalues on OOD inputs, yielding a clear spectral signature. We further provide analysis explicitly linking posterior covariance to distribution mismatch, establishing it as a reliable signal for OOD detection. To ensure tractability, we adopt a Jacobian-free subspace iteration method to estimate the leading eigenvalues using only forward evaluations of the denoiser. Empirically, EigenScore achieves state-of-the-art performance, with up to 2% AUROC improvement over the best baseline. Notably, it remains robust in near-OOD settings such as CIFAR-10 vs CIFAR-100, where existing diffusion-based methods often fail.

Computer Vision · Vision Models & Multimodal

Aryan Yazdan Parast, Parsa Hosseini, Hesam Asadollahzadeh, Arshia Soltani Moakhar, Basim Azam, Soheil Feizi, NAVEED AKHTAR

Object hallucination in Multimodal Large Language Models (MLLMs) is a persistent failure mode that causes the model to perceive objects absent in the image. This weakness of MLLMs is currently studied using static benchmarks with fixed visual scenarios, which preempts the possibility of uncovering model-specific or unanticipated hallucination vulnerabilities. We introduce GHOST (Generating Hallucinations via Optimizing Stealth Tokens), a method designed to stress-test MLLMs by actively generating images that induce hallucination. GHOST is fully automatic and requires no human supervision or prior knowledge. It operates by optimizing in the image embedding space to mislead the model while keeping the target object absent, and then guiding a diffusion model conditioned on the embedding to generate natural-looking images. The resulting images remain visually natural and close to the original input, yet introduce subtle misleading cues that cause the model to hallucinate. We evaluate our method across a range of models, including reasoning models like GLM-4.1V-Thinking, and achieve a hallucination success rate exceeding 28%, compared to around 1% in prior data-driven discovery methods. We confirm that the generated images are both high-quality and object-free through quantitative metrics and human evaluation. Also, GHOST uncovers transferable vulnerabilities: images optimized for Qwen2.5-VL induce hallucinations in GPT-4o at a 66.5% rate. Finally, we show that fine-tuning on our images mitigates hallucination, positioning GHOST as both a diagnostic and corrective tool for building more reliable multimodal systems.

Applications · Everything Else

Shu Liu, Wenlin Chen, Weihao Li, Zheng Wang, Lijin Yang, Jianing Huang, YipinZhang, Zhongzhan Huang, Ze Cheng, Hao Yang

Diffusion-based planners have shown strong potential for autonomous driving by capturing multi-modal driving behaviors. A key challenge is how to effectively guide these models for safe and reactive planning in closed-loop settings, where the ego vehicle's actions influence future states. Recent work leverages typical expert driving behaviors (i.e., anchors) to guide diffusion planners but relies on a truncated diffusion schedule that introduces an asymmetry between the forward and denoising processes, diverging from the core principles of diffusion models. To address this, we introduce BridgeDrive, a novel anchor-guided diffusion bridge policy for closed-loop trajectory planning. Our approach formulates planning as a diffusion bridge that directly transforms coarse anchor trajectories into refined, context-aware plans, ensuring theoretical consistency between the forward and reverse processes. BridgeDrive is compatible with efficient ODE solvers, enabling real-time deployment. We achieve state-of-the-art performance on the Bench2Drive closed-loop evaluation benchmark, improving the success rate by 7.72% and 2.45% over prior arts with PDM-Lite and LEAD datasets, respectively. Project page: https://github.com/shuliu-ethz/BridgeDrive.

Jaeyeon Kim, Lee Kit, Carles Domingo i Enrich, Yilun Du, Sham Kakade, Timothy Ngotiaoco, Sitan Chen, Michael Albergo

Masked diffusion models (MDMs) have recently emerged as a promising alternative to autoregressive models over discrete domains. MDMs generate sequences in an any-order, parallel fashion, enabling fast inference and strong performance on non-causal tasks. However, a crucial limitation is that they do not support token insertions and are thus limited to *fixed-length* generations. To this end, we introduce **Flex**ible **M**asked **D**iffusion **M**odels (FlexMDMs), a discrete diffusion paradigm that simultaneously can model sequences of flexible length while provably retaining MDMs' flexibility of any-order inference. Grounded in an extension of the stochastic interpolant framework, FlexMDMs generate sequences by inserting mask tokens and unmasking them. Empirically, we show that FlexMDMs match MDMs in perplexity while modeling length statistics with much higher fidelity. On a synthetic maze planning task, they achieve $\approx$ 60\% higher success rate than MDM baselines. Finally, we show pretrained MDMs can easily be *retrofitted* into FlexMDMs: on 16 H100s, it takes only three days to fine-tune LLaDA-8B into a FlexMDM, achieving superior performance on math (GSM8K, 58\%$\to$67\%) and code infilling performance (52\%$\to$65\%).

General Machine Learning · Probabilistic Methods

David Huk, Theodoros Damoulas

Copulas are a fundamental tool for modelling multivariate dependencies in data, forming the method of choice in diverse fields and applications. However, the adoption of existing models for multimodal and high-dimensional dependencies is hindered by restrictive assumptions and poor scaling. In this work, we present methods for modelling copulas based on the principles of diffusions and flows. We design two processes that progressively forget inter-variable dependencies while leaving dimension-wise distributions unaffected, provably defining valid copulas at all times. We show how to obtain copula models by learning to remember the forgotten dependencies from each process, theoretically recovering the true copula at optimality. The first instantiation of our framework focuses on direct density estimation, while the second specialises in expedient sampling. Empirically, we demonstrate the superior performance of our proposed methods over state-of-the-art copula approaches in modelling complex and high-dimensional dependencies from scientific datasets and images. Our work enhances the representational power of copula models, empowering applications and paving the way for their adoption on larger scales and more challenging domains.