Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View

Reinforcement learning (RL) post-training provides a direct way to align diffusion models with human preferences and task-specific rewards. However, current RL algorithms for diffusion models remain fragmented: reverse-trajectory methods rely on discretized likelihood ratios, whereas forward-matching methods train on reward-labeled noising versions of the rollout samples. This paper shows that these seemingly different losses arise from a single path-space principle. Starting from the regularized diffusion-RL objective, we use importance sampling between sampling SDEs to obtain an explicit policy-gradient estimator on trajectory space. The estimator contains the stochastic Itô integral underlying Flow-GRPO-type updates; we derive an equivalent variance-reduced value-gradient form that recovers the forward-matching structure of AWM and DiffusionNFT. This identifies the empirical gap between these method families as a variance-reduction effect rather than a difference in RL principle. The derivation yields a unified design space organized by value-gradient estimation, weight functions, and sampling choices. Within this space, we propose a multi-sample KDE value-gradient estimator that reuses rollout groups, together with scale-bounded weight families that retain stable existing recipes while excluding singular ones. Experiments on SD3.5-M and Qwen-Image models validate the variance-reduction explanation and show that the resulting recipe improves over prior diffusion-RL baselines.

AREX: Towards a Recursively Self-Improving Agent for Deep Research

Deep research requires agents to find answers that jointly satisfy multiple constraints. Discovering such answers is costly, whereas verifying a candidate can often be decomposed into tractable constraint-wise checks. This discovery--verification asymmetry suggests that a research agent should do more than simply search longer: it should recursively improve its current answer by verifying intermediate results and using the partially verified state to guide subsequent refinement. We introduce AREX, a family of Recursively Self-Improving (RSI) deep research agents. AREX alternates between an inner research loop that gathers evidence and constructs a provisional answer, and an outer self-improvement loop that audits the answer constraint-wise, identifies unresolved claims, and launches targeted follow-up research. To sustain RSI over long horizons, AREX learns an autonomous context-update tool that compresses growing interaction history into a compact improvement state preserving verified evidence and unresolved constraints, without relying on an external model. We train AREX on verified synthetic tasks and high-quality trajectories through agentic mid-training and long-horizon reinforcement learning. To mitigate sparse final rewards during long horizon learning, we emphasize key steps where decisive evidence is acquired or erroneous research directions are corrected. We instantiate a dense 4B model and a 122B-A10B Mixture-of-Experts model. Across BrowseComp, WideSearch, DeepSearchQA, Humanity's Last Exam (HLE), and other reasoning and tool-use benchmarks, AREX substantially outperforms comparable-scale baselines and remains competitive with models using substantially more activated parameters.

Muse: Representation Geometry of Muon Beyond Normalized Momentum

Muon-style optimizers apply a polar map to matrix momentum, but their updates also depend on the representation of each parameter block before orthogonalization. We study this representation choice as a form of optimizer geometry and introduce {\method}, a family of Muon-style optimizers that shares the same momentum rule and Newton--Schulz backend across native, nearest-square, skinny, and vector representations. Each Frobenius-isometric representation induces a distinct polar steepest-descent geometry, in which the shorter matrix dimension determines the number of supported singular channels, the pullback scaling, and the constants in stochastic nonconvex convergence bounds. In a teacher--student model, curvature collapse and an isotropic Marchenko--Pastur spectral profile connect early-stage dissipation to the represented nuclear-to-squared-Frobenius norm ratio. Pretraining experiments on LLaMA2-130M and LLaMA2-600M, together with fixed-momentum diagnostics, show that balanced non-native representations can match the performance of the native representation, whereas reducing the shorter dimension weakens the scaling and singular-channel support, leading to behavior that increasingly resembles normalized momentum.

Parallel Rollout Approximation for Pixel-Space Autoregressive Image Generation

Pixel-space continuous-token autoregressive (AR) generation directly models images as sequences of raw pixel patches, avoiding discrete tokenization or a separately pretrained tokenizer. However, it faces coupled challenges: high-dimensional patch generation causes large single-step errors, and teacher-forced training creates a train--inference gap that makes these errors accumulate across AR steps. Existing fixes such as $x$-prediction and input noise injection only partially mitigate these issues. Exact rollout training better matches inference-time conditions, but is impractical due to prohibitively slow sequential sampling. We propose \emph{Parallel Rollout Approximation} (PRA), a scalable framework that addresses both challenges jointly. PRA generates low-dimensional intermediate states instead of high-dimensional pixel patches, then maps them back to pixel-space tokens with a pixel decoder, preserving a pixel-in, pixel-out AR interface. It also constructs inference-like pixel inputs through the same intermediate-state-to-pixel path used at inference, independently across positions, approximating the pixel-feedback interface encountered during inference-time rollout while retaining parallel teacher-forced training. On class-conditional ImageNet-1K generation at $256\times256$ resolution, PRA-S with 135M parameters achieves an FID of 2.58, surpassing the previous billion-scale pixel-space AR result of 3.60. Scaling to PRA-L with 511M parameters further improves FID to 1.94, establishing a new state of the art among pixel-space AR models. Beyond generation, PRA achieves higher ImageNet classification probing accuracy than other AR and diffusion baselines, suggesting its potential for unified pixel-space image generation and understanding.

Ouroboros-Spatial: Closing the Data-Model Loop for Spatial Reasoning

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

One LR Doesn't Fit All: Heavy-Tail Guided Layerwise Learning Rates for LLMs

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their effectiveness as the backbone of Large Language Models (LLMs). In this paper, we introduce Layerwise Learning Rate (LLR), an adaptive scheme that assigns distinct learning rates to individual Transformer layers. Our method is grounded in Heavy-Tailed Self-Regularization (HT-SR) theory, which characterizes the empirical spectral density (ESD) of weight correlation matrices to quantify heavy-tailedness. Layers with weaker heavy-tailedness are assigned larger learning rates to accelerate their training, while layers with stronger heavy-tailedness receive smaller learning rates. By tailoring learning rates in this manner, LLR promotes balanced training across layers, leading to faster convergence and improved generalization. Extensive experiments across architectures (from LLaMA to GPT-nano), optimizers (AdamW and Muon), and parameter scales (60M-1B) demonstrate that LLR achieves up to 1.5x training speedup and outperforms baselines, notably raising average zero-shot accuracy from 47.09% to 49.02%. A key advantage of LLR is its low tuning overhead: it transfers nearly optimal LR settings directly from the uniform baseline. Code is available at https://github.com/hed-ucas/Layer-wise-Learning-Rate.

Quotient-Space Diffusion Models

Diffusion-based generative models have reformed generative AI, and have enabled new capabilities in the science domain, for example, generating 3D structures of molecules. Due to the intrinsic problem structure of certain tasks, there is often a symmetry in the system, which identifies objects that can be converted by a group action as equivalent, hence the target distribution is essentially defined on the quotient space with respect to the group. In this work, we establish a formal framework for diffusion modeling on a general quotient space, and apply it to molecular structure generation which follows the special Euclidean group $\text{SE}(3)$ symmetry. The framework reduces the necessity of learning the component corresponding to the group action, hence simplifies learning difficulty over conventional group-equivariant diffusion models, and the sampler guarantees recovering the target distribution, while heuristic alignment strategies lack proper samplers. The arguments are empirically validated on structure generation for small molecules and proteins, indicating that the principled quotient-space diffusion model provides a new framework that outperforms previous symmetry treatments.

Evaluation-driven Scaling for Scientific Discovery

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

In-Place Test-Time Training

The static ``train then deploy" paradigm fundamentally limits Large Language Models (LLMs) from dynamically adapting their weights in response to continuous streams of new information inherent in real-world tasks. Test-Time Training (TTT) offers a compelling alternative by updating a subset of model parameters (fast weights) at inference time, yet its potential in the current LLM ecosystem is hindered by critical barriers including architectural incompatibility, computational inefficiency and misaligned fast weight objectives for language modeling. In this work, we introduce In-Place Test-Time Training (In-Place TTT), a framework that seamlessly endows LLMs with Test-Time Training ability. In-Place TTT treats the final projection matrix of the ubiquitous MLP blocks as its adaptable fast weights, enabling a ``drop-in" enhancement for LLMs without costly retraining from scratch. Furthermore, we replace TTT's generic reconstruction objective with a tailored, theoretically-grounded objective explicitly aligned with the Next-Token-Prediction task governing autoregressive language modeling. This principled objective, combined with an efficient chunk-wise update mechanism, results in a highly scalable algorithm compatible with context parallelism. Extensive experiments validate our framework's effectiveness: as an in-place enhancement, it enables a 4B-parameter model to achieve superior performance on tasks with contexts up to 128k, and when pretrained from scratch, it consistently outperforms competitive TTT-related approaches. Ablation study results further provide deeper insights on our design choices. Collectively, our results establish In-Place TTT as a promising step towards a paradigm of continual learning in LLMs.

AgentFactory: A Self-Evolving Framework Through Executable Subagent Accumulation and Reuse

Building LLM-based agents has become increasingly important. Recent works on LLM-based agent self-evolution primarily record successful experiences as textual prompts or reflections, which cannot reliably guarantee efficient task re-execution in complex scenarios. We propose AgentFactory, a new self-evolution paradigm that preserves successful task solutions as executable subagent code rather than textual experience. Crucially, these subagents are continuously refined based on execution feedback, becoming increasingly robust and efficient as more tasks are encountered. Saved subagents are pure Python code with standardized documentation, enabling portability across any Python-capable system. We demonstrate that AgentFactory enables continuous capability accumulation: its library of executable subagents grows and improves over time, progressively reducing the effort required for similar tasks without manual intervention. Our implementation is open-sourced at https://github.com/zzatpku/AgentFactory, and our demonstration video is available at https://youtu.be/iKSsuAXJHW0.