Normalizing Flows with Iterative Denoising

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks, making them viable alternatives to other methods such as diffusion models. In this work, we further advance the state of Normalizing Flow generative models by introducing iterative TARFlow (iTARFlow). Unlike diffusion models, iTARFlow maintains a fully end-to-end, likelihood-based objective during training. During sampling, it performs autoregressive generation followed by an iterative denoising procedure inspired by diffusion-style methods. Through extensive experiments, we show that iTARFlow achieves competitive performance across ImageNet resolutions of 64, 128, and 256 pixels, demonstrating its potential as a strong generative model and advancing the frontier of Normalizing Flows. In addition, we analyze the characteristic artifacts produced by iTARFlow, offering insights that may shed light on future improvements. Code is available at https://github.com/apple/ml-itarflow.

Grokking of Diffusion Models: Case Study on Modular Addition

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization after overfitting--on modular addition, enabling controlled analysis of their internal computations. We study this phenomenon across two levels of data regime. In a single-image regime, mechanistic dissection reveals that the model implements modular addition by composing periodic representations of individual operands. In a diverse-image regime with high intraclass variability, we find that the model leverages its iterative sampling process to partition the task into an arithmetic computation phase followed by a visual denoising phase, separated by a critical timestep threshold. Our work provides the mechanistic decomposition of algorithmic learning in diffusion models, revealing how these models bridge continuous pixel-space generation and discrete symbolic reasoning.

Pretrained Multilingual Transformers Reveal Quantitative Distance Between Human Languages

Understanding the distance between human languages is central to linguistics, anthropology, and tracing human evolutionary history. Yet, while linguistics has long provided rich qualitative accounts of cross-linguistic variation, a unified and scalable quantitative approach to measuring language distance remains lacking. In this paper, we introduce a method that leverages pretrained multilingual language models as systematic instruments for linguistic measurement. Specifically, we show that the spontaneously emerged attention mechanisms of these models provide a robust, tokenization-agnostic measure of cross-linguistic distance, termed Attention Transport Distance (ATD). By treating attention matrices as probability distributions and measuring their geometric divergence via optimal transport, we quantify the representational distance between languages during translation. Applying ATD to a large and diverse set of languages, we demonstrate that the resulting distances recover established linguistic groupings with high fidelity and reveal patterns aligned with geographic and contact-induced relationships. Furthermore, incorporating ATD as a regularizer improves transfer performance in low-resource machine translation. Our results establish a principled foundation for testing linguistic hypotheses using artificial neural networks. This framework transforms multilingual models into powerful tools for quantitative linguistic discovery, facilitating more equitable multilingual AI.

OmniGuide: Universal Guidance Fields for Enhancing Generalist Robot Policies

Vision-language-action(VLA) models have shown great promise as generalist policies for a large range of relatively simple tasks. However, they demonstrate limited performance on more complex tasks, such as those requiring complex spatial or semantic understanding, manipulation in clutter, or precise manipulation. We propose OMNIGUIDE, a flexible framework that improves VLA performance on such tasks by leveraging arbitrary sources of guidance, such as 3D foundation models, semantic-reasoning VLMs, and human pose models. We show how many kinds of guidance can be naturally expressed as differentiable energy functions with task-specific attractors and repellers located in 3D space, that influence the sampling of VLA actions. In this way, OMNIGUIDE enables guidance sources with complementary task-relevant strengths to improve a VLA model's performance on challenging tasks. Extensive experiments in both simulation and real-world environments, across diverse sources of guidance, demonstrate that OMNIGUIDE enhances the performance of state-of-the-art generalist policies (e.g., $π_{0.5}$, GR00T N1.6) significantly across success and safety rates. Critically, our unified framework matches or surpasses the performance of prior methods designed to incorporate specific sources of guidance into VLA policies. Project Page: $\href{https://omniguide.github.io/}{this \; url}$

The Coupling Within: Flow Matching via Distilled Normalizing Flows

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define the flow matching (FM) regression loss. While FM training defaults usually to independent coupling, recent works show that adaptive couplings informed by noise/data distributions (e.g., via optimal transport, OT) improve both model training and inference. We radicalize this insight by shifting the paradigm: rather than computing adaptive couplings directly, we use distilled couplings from a different, pretrained model capable of placing noise and data spaces in bijection -- a property intrinsic to normalizing flows (NF) through their maximum likelihood and invertibility requirements. Leveraging recent advances in NF image generation via auto-regressive (AR) blocks, we propose Normalized Flow Matching (NFM), a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models. These students achieve the best of both worlds: significantly outperforming flow models trained with independent or even OT couplings, while also improving on the teacher AR-NF model.

Multiplex Thinking: Reasoning via Token-wise Branch-and-Merge

Large language models often solve complex reasoning tasks more effectively with Chain-of-Thought (CoT), but at the cost of long, low-bandwidth token sequences. Humans, by contrast, often reason softly by maintaining a distribution over plausible next steps. Motivated by this, we propose Multiplex Thinking, a stochastic soft reasoning mechanism that, at each thinking step, samples K candidate tokens and aggregates their embeddings into a single continuous multiplex token. This preserves the vocabulary embedding prior and the sampling dynamics of standard discrete generation, while inducing a tractable probability distribution over multiplex rollouts. Consequently, multiplex trajectories can be directly optimized with on-policy reinforcement learning (RL). Importantly, Multiplex Thinking is self-adaptive: when the model is confident, the multiplex token is nearly discrete and behaves like standard CoT; when it is uncertain, it compactly represents multiple plausible next steps without increasing sequence length. Across challenging math reasoning benchmarks, Multiplex Thinking consistently outperforms strong discrete CoT and RL baselines from Pass@1 through Pass@1024, while producing shorter sequences. The code and checkpoints are available at https://github.com/GMLR-Penn/Multiplex-Thinking.

One Layer Is Enough: Adapting Pretrained Visual Encoders for Image Generation

Visual generative models (e.g., diffusion models) typically operate in compressed latent spaces to balance training efficiency and sample quality. In parallel, there has been growing interest in leveraging high-quality pre-trained visual representations, either by aligning them inside VAEs or directly within the generative model. However, adapting such representations remains challenging due to fundamental mismatches between understanding-oriented features and generation-friendly latent spaces. Representation encoders benefit from high-dimensional latents that capture diverse hypotheses for masked regions, whereas generative models favor low-dimensional latents that must faithfully preserve injected noise. This discrepancy has led prior work to rely on complex objectives and architectures. In this work, we propose FAE (Feature Auto-Encoder), a simple yet effective framework that adapts pre-trained visual representations into low-dimensional latents suitable for generation using as little as a single attention layer, while retaining sufficient information for both reconstruction and understanding. The key is to couple two separate deep decoders: one trained to reconstruct the original feature space, and a second that takes the reconstructed features as input for image generation. FAE is generic; it can be instantiated with a variety of self-supervised encoders (e.g., DINO, SigLIP) and plugged into two distinct generative families: diffusion models and normalizing flows. Across class-conditional and text-to-image benchmarks, FAE achieves strong performance. For example, on ImageNet 256x256, our diffusion model with CFG attains a near state-of-the-art FID of 1.29 (800 epochs) and 1.70 (80 epochs). Without CFG, FAE reaches the state-of-the-art FID of 1.48 (800 epochs) and 2.08 (80 epochs), demonstrating both high quality and fast learning.

DenseAnnotate: Enabling Scalable Dense Caption Collection for Images and 3D Scenes via Spoken Descriptions

With the rapid adoption of multimodal large language models (MLLMs) across diverse applications, there is a pressing need for task-centered, high-quality training data. A key limitation of current training datasets is their reliance on sparse annotations mined from the Internet or entered via manual typing that capture only a fraction of an image's visual content. Dense annotations are more valuable but remain scarce. Traditional text-based annotation pipelines are poorly suited for creating dense annotations: typing limits expressiveness, slows annotation speed, and underrepresents nuanced visual features, especially in specialized areas such as multicultural imagery and 3D asset annotation. In this paper, we present DenseAnnotate, an audio-driven online annotation platform that enables efficient creation of dense, fine-grained annotations for images and 3D assets. Annotators narrate observations aloud while synchronously linking spoken phrases to image regions or 3D scene parts. Our platform incorporates speech-to-text transcription and region-of-attention marking. To demonstrate the effectiveness of DenseAnnotate, we conducted case studies involving over 1,000 annotators across two domains: culturally diverse images and 3D scenes. We curate a human-annotated multi-modal dataset of 3,531 images, 898 3D scenes, and 7,460 3D objects, with audio-aligned dense annotations in 20 languages, including 8,746 image captions, 2,000 scene captions, and 19,000 object captions. Models trained on this dataset exhibit improvements of 5% in multilingual, 47% in cultural alignment, and 54% in 3D spatial capabilities. Our results show that our platform offers a feasible approach for future vision-language research and can be applied to various tasks and diverse types of data.

DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation

Diffusion large language models (dLLMs) are compelling alternatives to autoregressive (AR) models because their denoising models operate over the entire sequence. The global planning and iterative refinement features of dLLMs are particularly useful for code generation. However, current training and inference mechanisms for dLLMs in coding are still under-explored. To demystify the decoding behavior of dLLMs and unlock their potential for coding, we systematically investigate their denoising processes and reinforcement learning (RL) methods. We train a 7B dLLM, \textbf{DiffuCoder}, on 130B tokens of code. Using this model as a testbed, we analyze its decoding behavior, revealing how it differs from that of AR models: (1) dLLMs can decide how causal their generation should be without relying on semi-AR decoding, and (2) increasing the sampling temperature diversifies not only token choices but also their generation order. This diversity creates a rich search space for RL rollouts. For RL training, to reduce the variance of token log-likelihood estimates and maintain training efficiency, we propose \textbf{coupled-GRPO}, a novel sampling scheme that constructs complementary mask noise for completions used in training. In our experiments, coupled-GRPO significantly improves DiffuCoder's performance on code generation benchmarks (+4.4\% on EvalPlus) and reduces reliance on AR bias during decoding. Our work provides deeper insight into the machinery of dLLM generation and offers an effective, diffusion-native RL training framework. https://github.com/apple/ml-diffucoder.

Vid2Sim: Generalizable, Video-based Reconstruction of Appearance, Geometry and Physics for Mesh-free Simulation

Faithfully reconstructing textured shapes and physical properties from videos presents an intriguing yet challenging problem. Significant efforts have been dedicated to advancing such a system identification problem in this area. Previous methods often rely on heavy optimization pipelines with a differentiable simulator and renderer to estimate physical parameters. However, these approaches frequently necessitate extensive hyperparameter tuning for each scene and involve a costly optimization process, which limits both their practicality and generalizability. In this work, we propose a novel framework, Vid2Sim, a generalizable video-based approach for recovering geometry and physical properties through a mesh-free reduced simulation based on Linear Blend Skinning (LBS), offering high computational efficiency and versatile representation capability. Specifically, Vid2Sim first reconstructs the observed configuration of the physical system from video using a feed-forward neural network trained to capture physical world knowledge. A lightweight optimization pipeline then refines the estimated appearance, geometry, and physical properties to closely align with video observations within just a few minutes. Additionally, after the reconstruction, Vid2Sim enables high-quality, mesh-free simulation with high efficiency. Extensive experiments demonstrate that our method achieves superior accuracy and efficiency in reconstructing geometry and physical properties from video data.