Improving Data Efficiency for LLM Reinforcement Fine-tuning Through Difficulty-targeted Online Data Selection and Rollout Replay

Reinforcement learning (RL) has become an effective approach for fine-tuning large language models (LLMs), particularly to enhance their reasoning capabilities. However, RL fine-tuning remains highly resource-intensive, and existing work has largely overlooked the problem of data efficiency. In this paper, we propose two techniques to improve data efficiency in LLM RL fine-tuning: difficulty-targeted online data selection and rollout replay. We introduce the notion of adaptive difficulty to guide online data selection, prioritizing questions of moderate difficulty that are more likely to yield informative learning signals. To estimate adaptive difficulty efficiently, we develop an attention-based framework that requires rollouts for only a small reference set of questions. The adaptive difficulty of the remaining questions is then estimated based on their similarity to this set. To further reduce rollout cost, we introduce a rollout replay mechanism that reuses recent rollouts, lowering per-step computation while maintaining stable updates. Extensive experiments across 6 LLM-dataset combinations show that our method reduces RL fine-tuning time by 25% to 65% to reach the same level of performance as the original GRPO algorithm.

Restoration Score Distillation: From Corrupted Diffusion Pretraining to One-Step High-Quality Generation

Learning generative models from corrupted data is a fundamental yet persistently challenging task across scientific disciplines, particularly when access to clean data is limited or expensive. Denoising Score Distillation (DSD) \cite{chen2025denoising} recently introduced a novel and surprisingly effective strategy that leverages score distillation to train high-fidelity generative models directly from noisy observations. Building upon this foundation, we propose \textit{Restoration Score Distillation} (RSD), a principled generalization of DSD that accommodates a broader range of corruption types, such as blurred, incomplete, or low-resolution images. RSD operates by first pretraining a teacher diffusion model solely on corrupted data and subsequently distilling it into a single-step generator that produces high-quality reconstructions. Empirically, RSD consistently surpasses its teacher model across diverse restoration tasks on both natural and scientific datasets. Moreover, beyond standard diffusion objectives, the RSD framework is compatible with several corruption-aware training techniques such as Ambient Tweedie, Ambient Diffusion, and its Fourier-space variant, enabling flexible integration with recent advances in diffusion modeling. Theoretically, we demonstrate that in a linear regime, RSD recovers the eigenspace of the clean data covariance matrix from linear measurements, thereby serving as an implicit regularizer. This interpretation recasts score distillation not only as a sampling acceleration technique but as a principled approach to enhancing generative performance in severely degraded data regimes.

A Generative Framework for Causal Estimation via Importance-Weighted Diffusion Distillation

Estimating individualized treatment effects from observational data is a central challenge in causal inference, largely due to covariate imbalance and confounding bias from non-randomized treatment assignment. While inverse probability weighting (IPW) is a well-established solution to this problem, its integration into modern deep learning frameworks remains limited. In this work, we propose Importance-Weighted Diffusion Distillation (IWDD), a novel generative framework that combines the pretraining of diffusion models with importance-weighted score distillation to enable accurate and fast causal estimation-including potential outcome prediction and treatment effect estimation. We demonstrate how IPW can be naturally incorporated into the distillation of pretrained diffusion models, and further introduce a randomization-based adjustment that eliminates the need to compute IPW explicitly-thereby simplifying computation and, more importantly, provably reducing the variance of gradient estimates. Empirical results show that IWDD achieves state-of-the-art out-of-sample prediction performance, with the highest win rates compared to other baselines, significantly improving causal estimation and supporting the development of individualized treatment strategies. We will release our PyTorch code for reproducibility and future research.

FreqMoE: Dynamic Frequency Enhancement for Neural PDE Solvers

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the sparsity of high-frequency signals limits computational efficiency for high-dimensional inputs, and fixed-pattern truncation often causes high-frequency signal loss, reducing performance in scenarios such as high-resolution inputs or long-term predictions. To address these challenges, we propose FreqMoE, an efficient and progressive training framework that exploits the dependency of high-frequency signals on low-frequency components. The model first learns low-frequency weights and then applies a sparse upward-cycling strategy to construct a mixture of experts (MoE) in the frequency domain, effectively extending the learned weights to high-frequency regions. Experiments on both regular and irregular grid PDEs demonstrate that FreqMoE achieves up to 16.6% accuracy improvement while using merely 2.1% parameters (47.32x reduction) compared to dense FNO. Furthermore, the approach demonstrates remarkable stability in long-term predictions and generalizes seamlessly to various FNO variants and grid structures, establishing a new ``Low frequency Pretraining, High frequency Fine-tuning'' paradigm for solving PDEs.

Galaxy Walker: Geometry-aware VLMs For Galaxy-scale Understanding

Modern vision-language models (VLMs) develop patch embedding and convolution backbone within vector space, especially Euclidean ones, at the very founding. When expanding VLMs to a galaxy scale for understanding astronomical phenomena, the integration of spherical space for planetary orbits and hyperbolic spaces for black holes raises two formidable challenges. a) The current pre-training model is confined to Euclidean space rather than a comprehensive geometric embedding. b) The predominant architecture lacks suitable backbones for anisotropic physical geometries. In this paper, we introduced Galaxy-Walker, a geometry-aware VLM, for the universe-level vision understanding tasks. We proposed the geometry prompt that generates geometry tokens by random walks across diverse spaces on a multi-scale physical graph, along with a geometry adapter that compresses and reshapes the space anisotropy in a mixture-of-experts manner. Extensive experiments demonstrate the effectiveness of our approach, with Galaxy-Walker achieving state-of-the-art performance in both galaxy property estimation ($R^2$ scores up to $0.91$) and morphology classification tasks (up to $+0.17$ F1 improvement in challenging features), significantly outperforming both domain-specific models and general-purpose VLMs.

Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generation

Diffusion models have achieved remarkable success in generating high-resolution, realistic images across diverse natural distributions. However, their performance heavily relies on high-quality training data, making it challenging to learn meaningful distributions from corrupted samples. This limitation restricts their applicability in scientific domains where clean data is scarce or costly to obtain. In this work, we introduce denoising score distillation (DSD), a surprisingly effective and novel approach for training high-quality generative models from low-quality data. DSD first pretrains a diffusion model exclusively on noisy, corrupted samples and then distills it into a one-step generator capable of producing refined, clean outputs. While score distillation is traditionally viewed as a method to accelerate diffusion models, we show that it can also significantly enhance sample quality, particularly when starting from a degraded teacher model. Across varying noise levels and datasets, DSD consistently improves generative performancewe summarize our empirical evidence in Fig. 1. Furthermore, we provide theoretical insights showing that, in a linear model setting, DSD identifies the eigenspace of the clean data distributions covariance matrix, implicitly regularizing the generator. This perspective reframes score distillation as not only a tool for efficiency but also a mechanism for improving generative models, particularly in low-quality data settings.

Enhancing and Accelerating Diffusion-Based Inverse Problem Solving through Measurements Optimization

Diffusion models have recently demonstrated notable success in solving inverse problems. However, current diffusion model-based solutions typically require a large number of function evaluations (NFEs) to generate high-quality images conditioned on measurements, as they incorporate only limited information at each step. To accelerate the diffusion-based inverse problem-solving process, we introduce \textbf{M}easurements \textbf{O}ptimization (MO), a more efficient plug-and-play module for integrating measurement information at each step of the inverse problem-solving process. This method is comprehensively evaluated across eight diverse linear and nonlinear tasks on the FFHQ and ImageNet datasets. By using MO, we establish state-of-the-art (SOTA) performance across multiple tasks, with key advantages: (1) it operates with no more than 100 NFEs, with phase retrieval on ImageNet being the sole exception; (2) it achieves SOTA or near-SOTA results even at low NFE counts; and (3) it can be seamlessly integrated into existing diffusion model-based solutions for inverse problems, such as DPS \cite{chung2022diffusion} and Red-diff \cite{mardani2023variational}. For example, DPS-MO attains a peak signal-to-noise ratio (PSNR) of 28.71 dB on the FFHQ 256 dataset for high dynamic range imaging, setting a new SOTA benchmark with only 100 NFEs, whereas current methods require between 1000 and 4000 NFEs for comparable performance.

Identifying General Mechanism Shifts in Linear Causal Representations

We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least $d$ environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than $d$ of them, since the number of latent factors $d$ could be very large. In this work, we consider precisely such a setting, where we allow a smaller than $d$ number of environments, and also allow for very coarse interventions that can very coarsely \textit{change the entire causal graph over the latent factors}. On the flip side, we relax what we wish to extract to simply the \textit{list of nodes that have shifted between one or more environments}. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset. The code can be found at https://github.com/TianyuCodings/iLCS.

Conditional diffusions for neural posterior estimation

Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in situations where posteriors are intractable or likelihood functions are treated as "black boxes." Existing NPE methods typically rely on normalizing flows, which transform a base distributions into a complex posterior by composing many simple, invertible transformations. But flow-based models, while state of the art for NPE, are known to suffer from several limitations, including training instability and sharp trade-offs between representational power and computational cost. In this work, we demonstrate the effectiveness of conditional diffusions as an alternative to normalizing flows for NPE. Conditional diffusions address many of the challenges faced by flow-based methods. Our results show that, across a highly varied suite of benchmarking problems for NPE architectures, diffusions offer improved stability, superior accuracy, and faster training times, even with simpler, shallower models. These gains persist across a variety of different encoder or "summary network" architectures, as well as in situations where no summary network is required. The code will be publicly available at \url{https://github.com/TianyuCodings/cDiff}.

Automated Proof Generation for Rust Code via Self-Evolution

Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary obstacle lies in the severe lack of data - there is much less proof than code for LLMs to train upon. In this paper, we introduce SAFE, a novel framework that overcomes the lack of human-written proof to enable automated proof generation of Rust code. SAFE establishes a self-evolving cycle where data synthesis and fine-tuning collaborate to enhance the model capability, leveraging the definitive power of a symbolic verifier in telling correct proof from incorrect ones. SAFE also re-purposes the large number of synthesized incorrect proofs to train the self-debugging capability of the fine-tuned models, empowering them to fix incorrect proofs based on the verifier's feedback. SAFE demonstrates superior efficiency and precision compared to GPT-4o. Through tens of thousands of synthesized proofs and the self-debugging mechanism, we improve the capability of open-source models, initially unacquainted with formal verification, to automatically write proof for Rust code. This advancement leads to a significant improvement in performance, achieving a 70.50% accuracy rate in a benchmark crafted by human experts, a significant leap over GPT-4o's performance of 24.46%.