CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates

We consider the problem of validating whether a neural posterior estimate \( q(\theta \mid x) \) is an accurate approximation to the true, unknown true posterior \( p(\theta \mid x) \). Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the \emph{Conditional Localization Test} (CoLT), a principled method designed to detect discrepancies between \( p(\theta \mid x) \) and \( q(\theta \mid x) \) across the full range of conditioning inputs. Rather than relying on exhaustive comparisons or density estimation at every \( x \), CoLT learns a localization function that adaptively selects points $\theta_l(x)$ where the neural posterior $q$ deviates most strongly from the true posterior $p$ for that $x$. This approach is particularly advantageous in typical simulation-based inference settings, where only a single draw \( \theta \sim p(\theta \mid x) \) from the true posterior is observed for each conditioning input, but where the neural posterior \( q(\theta \mid x) \) can be sampled an arbitrary number of times. Our theoretical results establish necessary and sufficient conditions for assessing distributional equality across all \( x \), offering both rigorous guarantees and practical scalability. Empirically, we demonstrate that CoLT not only performs better than existing methods at comparing $p$ and $q$, but also pinpoints regions of significant divergence, providing actionable insights for model refinement. These properties position CoLT as a state-of-the-art solution for validating neural posterior estimates.

The surprising strength of weak classifiers for validating neural posterior estimates

Neural Posterior Estimation (NPE) has emerged as a powerful approach for amortized Bayesian inference when the true posterior $p(\theta \mid y)$ is intractable or difficult to sample. But evaluating the accuracy of neural posterior estimates remains challenging, with existing methods suffering from major limitations. One appealing and widely used method is the classifier two-sample test (C2ST), where a classifier is trained to distinguish samples from the true posterior $p(\theta \mid y)$ versus the learned NPE approximation $q(\theta \mid y)$. Yet despite the appealing simplicity of the C2ST, its theoretical and practical reliability depend upon having access to a near-Bayes-optimal classifier -- a requirement that is rarely met and, at best, difficult to verify. Thus a major open question is: can a weak classifier still be useful for neural posterior validation? We show that the answer is yes. Building on the work of Hu and Lei, we present several key results for a conformal variant of the C2ST, which converts any trained classifier's scores -- even those of weak or over-fitted models -- into exact finite-sample p-values. We establish two key theoretical properties of the conformal C2ST: (i) finite-sample Type-I error control, and (ii) non-trivial power that degrades gently in tandem with the error of the trained classifier. The upshot is that even weak, biased, or overfit classifiers can still yield powerful and reliable tests. Empirically, the Conformal C2ST outperforms classical discriminative tests across a wide range of benchmarks. These results reveal the under appreciated strength of weak classifiers for validating neural posterior estimates, establishing the conformal C2ST as a practical, theoretically grounded diagnostic for modern simulation-based inference.

Safeguarding Multimodal Knowledge Copyright in the RAG-as-a-Service Environment

As Retrieval-Augmented Generation (RAG) evolves into service-oriented platforms (Rag-as-a-Service) with shared knowledge bases, protecting the copyright of contributed data becomes essential. Existing watermarking methods in RAG focus solely on textual knowledge, leaving image knowledge unprotected. In this work, we propose AQUA, the first watermark framework for image knowledge protection in Multimodal RAG systems. AQUA embeds semantic signals into synthetic images using two complementary methods: acronym-based triggers and spatial relationship cues. These techniques ensure watermark signals survive indirect watermark propagation from image retriever to textual generator, being efficient, effective and imperceptible. Experiments across diverse models and datasets show that AQUA enables robust, stealthy, and reliable copyright tracing, filling a key gap in multimodal RAG protection.

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.