Apple-$π$: Benchmarking Thinking with Video Towards Law-Grounded Physical Intelligence

Modern video generation models are increasingly hailed as emerging world models with an internalized grasp of physical law. Yet existing benchmarks largely evaluate physical plausibility only at the output level, without verifying whether the model arrives there through a faithful, law-grounded reasoning process. We introduce Apple-PI, the first benchmark that anchors video-model evaluation explicitly in physical laws. Apple-PI comprises three components. 1) Orchard: a dataset of 400 videos covering ten canonical tasks in classical mechanics. It separates single-law tasks for confounder-free diagnosis from multi-law tasks for probing generalization. 2) Benchmark Protocol: a three-stage protocol based on scientific reasoning, including Perception, Formulation, and Deduction. It uses chain-of-frames prompting on infographic-annotated first frames, treating the generated video as the model's visible reasoning trace. 3) Evaluation Suite: a hybrid evaluation suite that combines MLLM-based subjective scoring with physics-law-grounded objective measures. This enables stage-resolved diagnosis of not only whether a model fails, but where it fails. Benchmarking 11 models shows that current video models remain far from reliable law-grounded world simulators, with the best video model scoring only 0.473. Our stage-, pillar-, and source-resolved analyses further expose a Perception-to-Formulation-to-Deduction bottleneck, weak multi-law state transfer, and a persistent Sim-to-Real gap. These findings position Apple-PI as a diagnostic foundation for guiding future video models toward world models with law-grounded physical intelligence.

Curvature-Guided Geometric Representation for Protein-Ligand Binding Affinity Prediction

Protein-ligand binding affinity (PLA) prediction is critical in drug discovery. Despite the notable advancements in machine learning-based approaches, existing methods struggle to jointly characterize local geometric organization and globally coordinated cross-molecular interactions, limiting their ability to model complex binding mechanisms. Here, we propose RicciBind, a geometric representation framework that integrates curvature-guided hierarchical structure learning with optimal transport (OT)-based cross-domain alignment to model molecular interactions. Specifically, RicciBind leverages Ricci curvature to capture local interaction tightness within molecular structures, enhancing structural awareness and organizing atomic interactions into curvature-aware hierarchical representations. An OT-based cluster matching mechanism then aligns protein and ligand clusters across heterogeneous domains under geometric constraints, enabling globally consistent correspondences and revealing higher-order interaction patterns beyond local neighborhoods. By coupling curvature-guided structure encoding with OT-driven cross-domain alignment, RicciBind effectively models complex interaction semantics and substantially improves both the accuracy and interpretability of binding affinity prediction. Extensive experiments demonstrate that RicciBind achieved superior predictive performance and generalization across PLA benchmarks and virtual screening tasks. Ablation studies further confirmed the essential role of Ricci curvature in enhancing molecular interaction representations.

Is Your Driving World Model an All-Around Player?

Today's driving world models can generate remarkably realistic dash-cam videos, yet no single model excels universally. Some generate photorealistic textures but violate basic physics; others maintain geometric consistency but fail when subjected to closed-loop planning. This disconnect exposes a critical gap: the field evaluates how real generated worlds appear, but rarely whether they behave realistically. We introduce WorldLens, a unified benchmark that measures world-model fidelity across the full spectrum, from pixel quality and 4D geometry to closed-loop driving and human perceptual alignment, through five complementary aspects and 24 standardized dimensions. Our evaluation of six representative models reveals that no existing approach dominates across all axes: texture-rich models violate geometry, geometry-aware models lack behavioral fidelity, and even the strongest performers achieve only 2-3 out of 10 on human realism ratings. To bridge algorithmic metrics with human perception, we further contribute WorldLens-26K, a 26,808-entry human-annotated preference dataset pairing numerical scores with textual rationales, and WorldLens-Agent, a vision-language evaluator distilled from these judgments that enables scalable, explainable auto-assessment. Together, the benchmark, dataset, and agent form a unified ecosystem for assessing generated worlds not merely by visual appeal, but by physical and behavioral fidelity.

Agentic World Modeling: Foundations, Capabilities, Laws, and Beyond

As AI systems move from generating text to accomplishing goals through sustained interaction, the ability to model environment dynamics becomes a central bottleneck. Agents that manipulate objects, navigate software, coordinate with others, or design experiments require predictive environment models, yet the term world model carries different meanings across research communities. We introduce a "levels x laws" taxonomy organized along two axes. The first defines three capability levels: L1 Predictor, which learns one-step local transition operators; L2 Simulator, which composes them into multi-step, action-conditioned rollouts that respect domain laws; and L3 Evolver, which autonomously revises its own model when predictions fail against new evidence. The second identifies four governing-law regimes: physical, digital, social, and scientific. These regimes determine what constraints a world model must satisfy and where it is most likely to fail. Using this framework, we synthesize over 400 works and summarize more than 100 representative systems spanning model-based reinforcement learning, video generation, web and GUI agents, multi-agent social simulation, and AI-driven scientific discovery. We analyze methods, failure modes, and evaluation practices across level-regime pairs, propose decision-centric evaluation principles and a minimal reproducible evaluation package, and outline architectural guidance, open problems, and governance challenges. The resulting roadmap connects previously isolated communities and charts a path from passive next-step prediction toward world models that can simulate, and ultimately reshape, the environments in which agents operate.

AnimationBench: Are Video Models Good at Character-Centric Animation?

Video generation has advanced rapidly, with recent methods producing increasingly convincing animated results. However, existing benchmarks-largely designed for realistic videos-struggle to evaluate animation-style generation with its stylized appearance, exaggerated motion, and character-centric consistency. Moreover, they also rely on fixed prompt sets and rigid pipelines, offering limited flexibility for open-domain content and custom evaluation needs. To address this gap, we introduce AnimationBench, the first systematic benchmark for evaluating animation image-to-video generation. AnimationBench operationalizes the Twelve Basic Principles of Animation and IP Preservation into measurable evaluation dimensions, together with Broader Quality Dimensions including semantic consistency, motion rationality, and camera motion consistency. The benchmark supports both a standardized close-set evaluation for reproducible comparison and a flexible open-set evaluation for diagnostic analysis, and leverages visual-language models for scalable assessment. Extensive experiments show that AnimationBench aligns well with human judgment and exposes animation-specific quality differences overlooked by realism-oriented benchmarks, leading to more informative and discriminative evaluation of state-of-the-art I2V models.

Prompt Relay: Inference-Time Temporal Control for Multi-Event Video Generation

Video diffusion models have achieved remarkable progress in generating high-quality videos. However, these models struggle to represent the temporal succession of multiple events in real-world videos and lack explicit mechanisms to control when semantic concepts appear, how long they persist, and the order in which multiple events occur. Such control is especially important for movie-grade video synthesis, where coherent storytelling depends on precise timing, duration, and transitions between events. When using a single paragraph-style prompt to describe a sequence of complex events, models often exhibit semantic entanglement, where concepts intended for different moments in the video bleed into one another, resulting in poor text-video alignment. To address these limitations, we propose Prompt Relay, an inference-time, plug-and-play method to enable fine-grained temporal control in multi-event video generation, requiring no architectural modifications and no additional computational overhead. Prompt Relay introduces a penalty into the cross-attention mechanism, so that each temporal segment attends only to its assigned prompt, allowing the model to represent one semantic concept at a time and thereby improving temporal prompt alignment, reducing semantic interference, and enhancing visual quality.

Demystifing Video Reasoning

Recent advances in video generation have revealed an unexpected phenomenon: diffusion-based video models exhibit non-trivial reasoning capabilities. Prior work attributes this to a Chain-of-Frames (CoF) mechanism, where reasoning is assumed to unfold sequentially across video frames. In this work, we challenge this assumption and uncover a fundamentally different mechanism. We show that reasoning in video models instead primarily emerges along the diffusion denoising steps. Through qualitative analysis and targeted probing experiments, we find that models explore multiple candidate solutions in early denoising steps and progressively converge to a final answer, a process we term Chain-of-Steps (CoS). Beyond this core mechanism, we identify several emergent reasoning behaviors critical to model performance: (1) working memory, enabling persistent reference; (2) self-correction and enhancement, allowing recovery from incorrect intermediate solutions; and (3) perception before action, where early steps establish semantic grounding and later steps perform structured manipulation. During a diffusion step, we further uncover self-evolved functional specialization within Diffusion Transformers, where early layers encode dense perceptual structure, middle layers execute reasoning, and later layers consolidate latent representations. Motivated by these insights, we present a simple training-free strategy as a proof-of-concept, demonstrating how reasoning can be improved by ensembling latent trajectories from identical models with different random seeds. Overall, our work provides a systematic understanding of how reasoning emerges in video generation models, offering a foundation to guide future research in better exploiting the inherent reasoning dynamics of video models as a new substrate for intelligence.

UniT: Unified Multimodal Chain-of-Thought Test-time Scaling

Unified models can handle both multimodal understanding and generation within a single architecture, yet they typically operate in a single pass without iteratively refining their outputs. Many multimodal tasks, especially those involving complex spatial compositions, multiple interacting objects, or evolving instructions, require decomposing instructions, verifying intermediate results, and making iterative corrections. While test-time scaling (TTS) has demonstrated that allocating additional inference compute for iterative reasoning substantially improves language model performance, extending this paradigm to unified multimodal models remains an open challenge. We introduce UniT, a framework for multimodal chain-of-thought test-time scaling that enables a single unified model to reason, verify, and refine across multiple rounds. UniT combines agentic data synthesis, unified model training, and flexible test-time inference to elicit cognitive behaviors including verification, subgoal decomposition, and content memory. Our key findings are: (1) unified models trained on short reasoning trajectories generalize to longer inference chains at test time; (2) sequential chain-of-thought reasoning provides a more scalable and compute-efficient TTS strategy than parallel sampling; (3) training on generation and editing trajectories improves out-of-distribution visual reasoning. These results establish multimodal test-time scaling as an effective paradigm for advancing both generation and understanding in unified models.

Error Analysis of Bayesian Inverse Problems with Generative Priors

Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to learn a bespoke prior for the problem at hand. In this article we present an analysis for such problems by presenting quantitative error bounds for minimum Wasserstein-2 generative models for the prior. We show that under some assumptions, the error in the posterior due to the generative prior will inherit the same rate as the prior with respect to the Wasserstein-1 distance. We further present numerical experiments that verify that aspects of our error analysis manifests in some benchmarks followed by an elliptic PDE inverse problem where a generative prior is used to model a non-stationary field.

BabyVision: Visual Reasoning Beyond Language

While humans develop core visual skills long before acquiring language, contemporary Multimodal LLMs (MLLMs) still rely heavily on linguistic priors to compensate for their fragile visual understanding. We uncovered a crucial fact: state-of-the-art MLLMs consistently fail on basic visual tasks that humans, even 3-year-olds, can solve effortlessly. To systematically investigate this gap, we introduce BabyVision, a benchmark designed to assess core visual abilities independent of linguistic knowledge for MLLMs. BabyVision spans a wide range of tasks, with 388 items divided into 22 subclasses across four key categories. Empirical results and human evaluation reveal that leading MLLMs perform significantly below human baselines. Gemini3-Pro-Preview scores 49.7, lagging behind 6-year-old humans and falling well behind the average adult score of 94.1. These results show despite excelling in knowledge-heavy evaluations, current MLLMs still lack fundamental visual primitives. Progress in BabyVision represents a step toward human-level visual perception and reasoning capabilities. We also explore solving visual reasoning with generation models by proposing BabyVision-Gen and automatic evaluation toolkit. Our code and benchmark data are released at https://github.com/UniPat-AI/BabyVision for reproduction.