Daily Papers

Physical AI models are evaluated on suites of benchmarks that differ across model reports, leaving the model-by-benchmark matrix sparse and the relationship between benchmarks unmeasured. We construct a matrix of 51 models on 12 physical AI benchmarks, selected from a registry of 51 benchmarks and 152 models by reporting density, combining scores from model cards and benchmark papers with our own evaluation runs under each benchmark's official protocol. We measure how much information the benchmarks share and show quantitative evidence of Redundancy. Redundancy affects reported rankings: collapsing the two substitute pairs into single columns moves 22 of 51 models by three or more places under an equally weighted average. We then select benchmarks greedily under a utility combining score dispersion with variance not explained by the already-selected set, and obtain a four-benchmark subset retaining 78.5\% of the utility of all 12, on which we fit a Bradley--Terry ranking. The procedure requires only benchmark-level scores with sufficient overlap and is not specific to physical AI.

Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used for large classes of noise distributions without ever knowing the underlying noise distribution. Similar to the original Noise2Score, the new approach is composed of two successive steps: score matching using perturbed noisy images, followed by a closed form image denoising formula via distribution-independent Tweedie's formula. This also suggests a systematic algorithm to estimate the noise model and noise parameters for a given noisy image data set. Through extensive experiments, we demonstrate that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.

Existing function-calling benchmarks focus on single-turn interactions. However, they overlook the complexity of real-world scenarios. To quantify how existing benchmarks address practical applications, we introduce DICE-SCORE, a metric that evaluates the dispersion of tool-related information such as function name and parameter values throughout the dialogue. Analyzing existing benchmarks through DICE-SCORE reveals notably low scores, highlighting the need for more realistic scenarios. To address this gap, we present DICE-BENCH, a framework that constructs practical function-calling datasets by synthesizing conversations through a tool graph that maintains dependencies across rounds and a multi-agent system with distinct personas to enhance dialogue naturalness. The final dataset comprises 1,607 high-DICE-SCORE instances. Our experiments on 19 LLMs with DICE-BENCH show that significant advances are still required before such models can be deployed effectively in real-world settings. Our code and data are all publicly available: https://snuhcc.github.io/DICE-Bench/.

Instruction tuning relies on large instruction-response corpora whose quality and composition strongly affect downstream performance. We propose Answer Divergence-Guided Selection (ADG), which selects instruction data based on the geometric structure of multi-sample outputs. ADG draws several high-temperature generations per instruction, maps responses into an embedding space, and computes an output divergence score that jointly encodes dispersion magnitude and shape anisotropy. High scores correspond to instructions whose answers are both far apart and multi-modal, rather than clustered paraphrases along a single direction. Across two backbones and three public instruction pools, fine-tuning on only 10K ADG-selected examples consistently outperforms strong selectors on six benchmarks spanning reasoning, knowledge, and coding. Analyses further show that both dispersion magnitude and shape anisotropy are necessary, supporting answer divergence as a practical signal for instruction data selection. Code and appendix are included in the supplementary materials.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

Score distillation of 2D diffusion models has proven to be a powerful mechanism to guide 3D optimization, for example enabling text-based 3D generation or single-view reconstruction. A common limitation of existing score distillation formulations, however, is that the outputs of the (mode-seeking) optimization are limited in diversity despite the underlying diffusion model being capable of generating diverse samples. In this work, inspired by the sampling process in denoising diffusion, we propose a score formulation that guides the optimization to follow generation paths defined by random initial seeds, thus ensuring diversity. We then present an approximation to adopt this formulation for scenarios where the optimization may not precisely follow the generation paths (e.g. a 3D representation whose renderings evolve in a co-dependent manner). We showcase the applications of our `Diverse Score Distillation' (DSD) formulation across tasks such as 2D optimization, text-based 3D inference, and single-view reconstruction. We also empirically validate DSD against prior score distillation formulations and show that it significantly improves sample diversity while preserving fidelity.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.

Score Distillation Sampling (SDS) has emerged as an effective technique for leveraging 2D diffusion priors for tasks such as text-to-3D generation. While powerful, SDS struggles with achieving fine-grained alignment to user intent. To overcome this, we introduce RewardSDS, a novel approach that weights noise samples based on alignment scores from a reward model, producing a weighted SDS loss. This loss prioritizes gradients from noise samples that yield aligned high-reward output. Our approach is broadly applicable and can extend SDS-based methods. In particular, we demonstrate its applicability to Variational Score Distillation (VSD) by introducing RewardVSD. We evaluate RewardSDS and RewardVSD on text-to-image, 2D editing, and text-to-3D generation tasks, showing significant improvements over SDS and VSD on a diverse set of metrics measuring generation quality and alignment to desired reward models, enabling state-of-the-art performance. Project page is available at https://itaychachy. github.io/reward-sds/.

Diffusion models have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose Score Augmentation (ScoreAug), a novel data augmentation framework specifically designed for diffusion models. Unlike conventional augmentation approaches that operate on clean data, ScoreAug applies transformations to noisy data, aligning with the inherent denoising mechanism of diffusion. Crucially, ScoreAug further requires the denoiser to predict the augmentation of the original target. This design establishes an equivariant learning objective, enabling the denoiser to learn scores across varied denoising spaces, thereby realizing what we term score augmentation. We also theoretically analyze the relationship between scores in different spaces under general transformations. In experiments, we extensively validate ScoreAug on multiple benchmarks including CIFAR-10, FFHQ, AFHQv2, and ImageNet, with results demonstrating significant performance improvements over baselines. Notably, ScoreAug effectively mitigates overfitting across diverse scenarios, such as varying data scales and model capacities, while exhibiting stable convergence properties. Another advantage of ScoreAug over standard data augmentation lies in its ability to circumvent data leakage issues under certain conditions. Furthermore, we show that ScoreAug can be synergistically combined with traditional data augmentation techniques to achieve additional performance gains.

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.

Score Distillation Sampling (SDS) is a recent but already widely popular method that relies on an image diffusion model to control optimization problems using text prompts. In this paper, we conduct an in-depth analysis of the SDS loss function, identify an inherent problem with its formulation, and propose a surprisingly easy but effective fix. Specifically, we decompose the loss into different factors and isolate the component responsible for noisy gradients. In the original formulation, high text guidance is used to account for the noise, leading to unwanted side effects. Instead, we train a shallow network mimicking the timestep-dependent denoising deficiency of the image diffusion model in order to effectively factor it out. We demonstrate the versatility and the effectiveness of our novel loss formulation through several qualitative and quantitative experiments, including optimization-based image synthesis and editing, zero-shot image translation network training, and text-to-3D synthesis.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.

Existing score-distilling text-to-3D generation techniques, despite their considerable promise, often encounter the view inconsistency problem. One of the most notable issues is the Janus problem, where the most canonical view of an object (e.g., face or head) appears in other views. In this work, we explore existing frameworks for score-distilling text-to-3D generation and identify the main causes of the view inconsistency problem -- the embedded bias of 2D diffusion models. Based on these findings, we propose two approaches to debias the score-distillation frameworks for view-consistent text-to-3D generation. Our first approach, called score debiasing, involves cutting off the score estimated by 2D diffusion models and gradually increasing the truncation value throughout the optimization process. Our second approach, called prompt debiasing, identifies conflicting words between user prompts and view prompts using a language model, and adjusts the discrepancy between view prompts and the viewing direction of an object. Our experimental results show that our methods improve the realism of the generated 3D objects by significantly reducing artifacts and achieve a good trade-off between faithfulness to the 2D diffusion models and 3D consistency with little overhead. Our project page is available at~https://susunghong.github.io/Debiased-Score-Distillation-Sampling/.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with proper designs, the evolution of neural networks during training can be accurately modeled by a series of kernel regression tasks. Furthermore, by applying an early-stopping rule for gradient descent and leveraging recent developments in neural tangent kernels, we establish the first generalization error (sample complexity) bounds for learning the score function with neural networks, despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.

Score Distillation Sampling (SDS) and its variants have been widely used for text-to-3D generation by distilling 2D image diffusion priors. However, the standard SDS objective is prone to severe mode collapse, frequently yielding over-smoothed and over-saturated results. Although recent advancements, such as Score Distillation via Inversion (SDI), mitigate these artifacts and produce visually sharper models, they ultimately fail to faithfully capture the full target distribution. In this work, we show that the bottleneck limiting the sampling capacity of SDI stems from its reliance on the posterior mean estimator, which is mathematically equivalent to a single-step Euler approximation of the deterministic reverse DDIM trajectory. To address this, we propose a naturally motivated extension termed Probability-Flow Distillation (PFD). We establish that PFD corresponds exactly to a Wasserstein gradient flow, thereby inducing principled distribution-matching dynamics. Finally, we show that PFD can synthesize 3D assets with fine-grained, high-fidelity details and achieve improved quality compared to existing methods.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

Score distillation sampling has been pivotal for integrating diffusion models into generation of complex visuals. Despite impressive results it suffers from mode collapse and lack of diversity. To cope with this challenge, we leverage the gradient flow interpretation of score distillation to propose Repulsive Score Distillation (RSD). In particular, we propose a variational framework based on repulsion of an ensemble of particles that promotes diversity. Using a variational approximation that incorporates a coupling among particles, the repulsion appears as a simple regularization that allows interaction of particles based on their relative pairwise similarity, measured e.g., via radial basis kernels. We design RSD for both unconstrained and constrained sampling scenarios. For constrained sampling we focus on inverse problems in the latent space that leads to an augmented variational formulation, that strikes a good balance between compute, quality and diversity. Our extensive experiments for text-to-image generation, and inverse problems demonstrate that RSD achieves a superior trade-off between diversity and quality compared with state-of-the-art alternatives.

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on image quality. We enforce the one-step image generator match the diffusion model at distribution level, by minimizing an approximate KL divergence whose gradient can be expressed as the difference between 2 score functions, one of the target distribution and the other of the synthetic distribution being produced by our one-step generator. The score functions are parameterized as two diffusion models trained separately on each distribution. Combined with a simple regression loss matching the large-scale structure of the multi-step diffusion outputs, our method outperforms all published few-step diffusion approaches, reaching 2.62 FID on ImageNet 64x64 and 11.49 FID on zero-shot COCO-30k, comparable to Stable Diffusion but orders of magnitude faster. Utilizing FP16 inference, our model generates images at 20 FPS on modern hardware.

Score Distillation Sampling (SDS) has emerged as the de facto approach for text-to-content generation in non-image domains. In this paper, we reexamine the SDS process and introduce a straightforward interpretation that demystifies the necessity for large Classifier-Free Guidance (CFG) scales, rooted in the distillation of an undesired noise term. Building upon our interpretation, we propose a novel Noise-Free Score Distillation (NFSD) process, which requires minimal modifications to the original SDS framework. Through this streamlined design, we achieve more effective distillation of pre-trained text-to-image diffusion models while using a nominal CFG scale. This strategic choice allows us to prevent the over-smoothing of results, ensuring that the generated data is both realistic and complies with the desired prompt. To demonstrate the efficacy of NFSD, we provide qualitative examples that compare NFSD and SDS, as well as several other methods.

While diffusion models show promising results in image editing given a target prompt, achieving both prompt fidelity and background preservation remains difficult. Recent works have introduced score distillation techniques that leverage the rich generative prior of text-to-image diffusion models to solve this task without additional fine-tuning. However, these methods often struggle with tasks such as object insertion. Our investigation of these failures reveals significant variations in gradient magnitude and spatial distribution, making hyperparameter tuning highly input-specific or unsuccessful. To address this, we propose two simple yet effective modifications: attention-based spatial regularization and gradient filtering-normalization, both aimed at reducing these variations during gradient updates. Experimental results show our method outperforms state-of-the-art score distillation techniques in prompt fidelity, improving successful edits while preserving the background. Users also preferred our method over state-of-the-art techniques across three metrics, and by 58-64% overall.

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. The PyTorch implementation is available at https://github.com/mingyuanzhou/SiD

The training of score-based diffusion models (SDMs) is based on score matching. The challenge of score matching is that it includes a computationally expensive Jacobian trace. While several methods have been proposed to avoid this computation, each has drawbacks, such as instability during training and approximating the learning as learning a denoising vector field rather than a true score. We propose a novel score matching variant, local curvature smoothing with Stein's identity (LCSS). The LCSS bypasses the Jacobian trace by applying Stein's identity, enabling regularization effectiveness and efficient computation. We show that LCSS surpasses existing methods in sample generation performance and matches the performance of denoising score matching, widely adopted by most SDMs, in evaluations such as FID, Inception score, and bits per dimension. Furthermore, we show that LCSS enables realistic image generation even at a high resolution of 1024 times 1024.

With significant advancements in diffusion models, addressing the potential risks of dataset bias becomes increasingly important. Since generated outputs directly suffer from dataset bias, mitigating latent bias becomes a key factor in improving sample quality and proportion. This paper proposes time-dependent importance reweighting to mitigate the bias for the diffusion models. We demonstrate that the time-dependent density ratio becomes more precise than previous approaches, thereby minimizing error propagation in generative learning. While directly applying it to score-matching is intractable, we discover that using the time-dependent density ratio both for reweighting and score correction can lead to a tractable form of the objective function to regenerate the unbiased data density. Furthermore, we theoretically establish a connection with traditional score-matching, and we demonstrate its convergence to an unbiased distribution. The experimental evidence supports the usefulness of the proposed method, which outperforms baselines including time-independent importance reweighting on CIFAR-10, CIFAR-100, FFHQ, and CelebA with various bias settings. Our code is available at https://github.com/alsdudrla10/TIW-DSM.

Current music similarity models typically compute a single, monolithic score, entangling distinct musical dimensions like melody, rhythm, and timbre. This limits user control and interpretability, making it impossible to execute nuanced queries. We introduce MERIT, a framework for learning disentangled, factor-specific music representations tailored to these three core dimensions. To overcome the lack of isolated musical variations in real-world audio, we use a novel training strategy that uses conditional audio generation and source-separated stems to strongly encourage single-factor variation in training data. Our evaluations demonstrate strong factor-wise disentanglement. Each head responds strongly to its intended perceptual dimension while remaining near chance on the others, a representational property that holds across both the synthetic training domain and independent real-world audio.

By leveraging the text-to-image diffusion priors, score distillation can synthesize 3D contents without paired text-3D training data. Instead of spending hours of online optimization per text prompt, recent studies have been focused on learning a text-to-3D generative network for amortizing multiple text-3D relations, which can synthesize 3D contents in seconds. However, existing score distillation methods are hard to scale up to a large amount of text prompts due to the difficulties in aligning pretrained diffusion prior with the distribution of rendered images from various text prompts. Current state-of-the-arts such as Variational Score Distillation finetune the pretrained diffusion model to minimize the noise prediction error so as to align the distributions, which are however unstable to train and will impair the model's comprehension capability to numerous text prompts. Based on the observation that the diffusion models tend to have lower noise prediction errors at earlier timesteps, we propose Asynchronous Score Distillation (ASD), which minimizes the noise prediction error by shifting the diffusion timestep to earlier ones. ASD is stable to train and can scale up to 100k prompts. It reduces the noise prediction error without changing the weights of pre-trained diffusion model, thus keeping its strong comprehension capability to prompts. We conduct extensive experiments across different 2D diffusion models, including Stable Diffusion and MVDream, and text-to-3D generators, including Hyper-iNGP, 3DConv-Net and Triplane-Transformer. The results demonstrate ASD's effectiveness in stable 3D generator training, high-quality 3D content synthesis, and its superior prompt-consistency, especially under large prompt corpus.

Existing score distillation methods are sensitive to classifier-free guidance (CFG) scale: manifested as over-smoothness or instability at small CFG scales, while over-saturation at large ones. To explain and analyze these issues, we revisit the derivation of Score Distillation Sampling (SDS) and decipher existing score distillation with the Wasserstein Generative Adversarial Network (WGAN) paradigm. With the WGAN paradigm, we find that existing score distillation either employs a fixed sub-optimal discriminator or conducts incomplete discriminator optimization, resulting in the scale-sensitive issue. We propose the Adversarial Score Distillation (ASD), which maintains an optimizable discriminator and updates it using the complete optimization objective. Experiments show that the proposed ASD performs favorably in 2D distillation and text-to-3D tasks against existing methods. Furthermore, to explore the generalization ability of our WGAN paradigm, we extend ASD to the image editing task, which achieves competitive results. The project page and code are at https://github.com/2y7c3/ASD.

Transferring knowledge from a cross-encoder teacher via Knowledge Distillation (KD) has become a standard paradigm for training retrieval models. While existing studies have largely focused on mining hard negatives to improve discrimination, the systematic composition of training data and the resulting teacher score distribution have received relatively less attention. In this work, we highlight that focusing solely on hard negatives prevents the student from learning the comprehensive preference structure of the teacher, potentially hampering generalization. To effectively emulate the teacher score distribution, we propose a Stratified Sampling strategy that uniformly covers the entire score spectrum. Experiments on in-domain and out-of-domain benchmarks confirm that Stratified Sampling, which preserves the variance and entropy of teacher scores, serves as a robust baseline, significantly outperforming top-K and random sampling in diverse settings. These findings suggest that the essence of distillation lies in preserving the diverse range of relative scores perceived by the teacher.

Meaningful scores for forecast verification are essential for developing reliable forecasts, and there has been much effort to develop scores that align well with human perceptions of forecast quality. Whilst many of these scores have intuitive interpretations, relatively little is known about how these scores rank different forecasts, and how scores reflect forecast error. We theoretically explore the behaviour of two scores that fall within the `neighbourhood' paradigm of spatial verification; the Fractions Skill Score (FSS) and Brier Divergence Skill Score (BDnSS). We investigate how each score ranks forecasts with two types of error; errors in the mean frequency (corresponding to intensity or shape errors) and errors in the standard deviation (corresponding to errors in spatial structure, such as blurring or excess noise). We find that under many situations the FSS assigns higher scores to forecasts that over-predict mean frequency, thus theoretically confirming the need to use the FSS with percentile thresholds. Both scores generally assign higher scores to forecasts with lower neighbourhood standard deviation, a reflection of the `double penalty' problem; however, we observe that size of this effect is larger for the BDnSS than the FSS, showing that the FSS under some situations is less susceptible to the double penalty problem than the BDnSS.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by 25-75\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around 6-8times better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with 32times fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

Text-driven diffusion-based video editing presents a unique challenge not encountered in image editing literature: establishing real-world motion. Unlike existing video editing approaches, here we focus on score distillation sampling to circumvent the standard reverse diffusion process and initiate optimization from videos that already exhibit natural motion. Our analysis reveals that while video score distillation can effectively introduce new content indicated by target text, it can also cause significant structure and motion deviation. To counteract this, we propose to match space-time self-similarities of the original video and the edited video during the score distillation. Thanks to the use of score distillation, our approach is model-agnostic, which can be applied for both cascaded and non-cascaded video diffusion frameworks. Through extensive comparisons with leading methods, our approach demonstrates its superiority in altering appearances while accurately preserving the original structure and motion.

Distribution Matching Distillation (DMD) is a promising score distillation technique that compresses pre-trained teacher diffusion models into efficient one-step or multi-step student generators. Nevertheless, its reliance on the reverse Kullback-Leibler (KL) divergence minimization potentially induces mode collapse (or mode-seeking) in certain applications. To circumvent this inherent drawback, we propose Adversarial Distribution Matching (ADM), a novel framework that leverages diffusion-based discriminators to align the latent predictions between real and fake score estimators for score distillation in an adversarial manner. In the context of extremely challenging one-step distillation, we further improve the pre-trained generator by adversarial distillation with hybrid discriminators in both latent and pixel spaces. Different from the mean squared error used in DMD2 pre-training, our method incorporates the distributional loss on ODE pairs collected from the teacher model, and thus providing a better initialization for score distillation fine-tuning in the next stage. By combining the adversarial distillation pre-training with ADM fine-tuning into a unified pipeline termed DMDX, our proposed method achieves superior one-step performance on SDXL compared to DMD2 while consuming less GPU time. Additional experiments that apply multi-step ADM distillation on SD3-Medium, SD3.5-Large, and CogVideoX set a new benchmark towards efficient image and video synthesis.

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

Text-to-3D generation has made remarkable progress recently, particularly with methods based on Score Distillation Sampling (SDS) that leverages pre-trained 2D diffusion models. While the usage of classifier-free guidance is well acknowledged to be crucial for successful optimization, it is considered an auxiliary trick rather than the most essential component. In this paper, we re-evaluate the role of classifier-free guidance in score distillation and discover a surprising finding: the guidance alone is enough for effective text-to-3D generation tasks. We name this method Classifier Score Distillation (CSD), which can be interpreted as using an implicit classification model for generation. This new perspective reveals new insights for understanding existing techniques. We validate the effectiveness of CSD across a variety of text-to-3D tasks including shape generation, texture synthesis, and shape editing, achieving results superior to those of state-of-the-art methods. Our project page is https://xinyu-andy.github.io/Classifier-Score-Distillation

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present variational score distillation (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i.e., 7.5). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed ProlificDreamer, can generate high rendering resolution (i.e., 512times512) and high-fidelity NeRF with rich structure and complex effects (e.g., smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic. Project page: https://ml.cs.tsinghua.edu.cn/prolificdreamer/

Distribution Matching Distillation (DMD) is a widely used paradigm for accelerating inference in few-step video diffusion models. However, DMD-style video distillation faces two coupled challenges: the fake score must track a continuously evolving generator, making training costly when frequent updates are required, while reverse-KL-style matching can be mode-seeking and conservative for preserving strong motion dynamics. To address these issues, we propose Score Gradient Matching Distillation (SGMD). SGMD adopts a fake-score perspective by directly optimizing the fake score toward the teacher, while using teacher stop-gradient Fisher as a stable distribution-matching objective. We provide a gradient analysis that motivates this objective choice under ideal tracking. Building on this, SGMD introduces a pair of dual potentials: negative-residual (NR) for outer-loop correction and residual-contraction (RC) for inner-loop tracking. Empirically, compared to DMD2, SGMD achieves an approximately sim 3times training speedup and substantially improves motion dynamics for 4-step distilled models while preserving temporal consistency. A human study confirms that SGMD is preferred in motion quality and overall preference, while visual quality and text alignment remain comparable. Code is available at https://github.com/ModelTC/LightX2V.

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

Score distillation has emerged as one of the most prevalent approaches for text-to-3D asset synthesis. Essentially, score distillation updates 3D parameters by lifting and back-propagating scores averaged over different views. In this paper, we reveal that the gradient estimation in score distillation is inherent to high variance. Through the lens of variance reduction, the effectiveness of SDS and VSD can be interpreted as applications of various control variates to the Monte Carlo estimator of the distilled score. Motivated by this rethinking and based on Stein's identity, we propose a more general solution to reduce variance for score distillation, termed Stein Score Distillation (SSD). SSD incorporates control variates constructed by Stein identity, allowing for arbitrary baseline functions. This enables us to include flexible guidance priors and network architectures to explicitly optimize for variance reduction. In our experiments, the overall pipeline, dubbed SteinDreamer, is implemented by instantiating the control variate with a monocular depth estimator. The results suggest that SSD can effectively reduce the distillation variance and consistently improve visual quality for both object- and scene-level generation. Moreover, we demonstrate that SteinDreamer achieves faster convergence than existing methods due to more stable gradient updates.

Accelerating diffusion model sampling is crucial for efficient AIGC deployment. While diffusion distillation methods -- based on distribution matching and trajectory matching -- reduce sampling to as few as one step, they fall short on complex tasks like text-to-image generation. Few-step generation offers a better balance between speed and quality, but existing approaches face a persistent trade-off: distribution matching lacks flexibility for multi-step sampling, while trajectory matching often yields suboptimal image quality. To bridge this gap, we propose learning few-step diffusion models by Trajectory Distribution Matching (TDM), a unified distillation paradigm that combines the strengths of distribution and trajectory matching. Our method introduces a data-free score distillation objective, aligning the student's trajectory with the teacher's at the distribution level. Further, we develop a sampling-steps-aware objective that decouples learning targets across different steps, enabling more adjustable sampling. This approach supports both deterministic sampling for superior image quality and flexible multi-step adaptation, achieving state-of-the-art performance with remarkable efficiency. Our model, TDM, outperforms existing methods on various backbones, such as SDXL and PixArt-alpha, delivering superior quality and significantly reduced training costs. In particular, our method distills PixArt-alpha into a 4-step generator that outperforms its teacher on real user preference at 1024 resolution. This is accomplished with 500 iterations and 2 A800 hours -- a mere 0.01% of the teacher's training cost. In addition, our proposed TDM can be extended to accelerate text-to-video diffusion. Notably, TDM can outperform its teacher model (CogVideoX-2B) by using only 4 NFE on VBench, improving the total score from 80.91 to 81.65. Project page: https://tdm-t2x.github.io/

Text-to-3D generation has shown rapid progress in recent days with the advent of score distillation, a methodology of using pretrained text-to-2D diffusion models to optimize neural radiance field (NeRF) in the zero-shot setting. However, the lack of 3D awareness in the 2D diffusion models destabilizes score distillation-based methods from reconstructing a plausible 3D scene. To address this issue, we propose 3DFuse, a novel framework that incorporates 3D awareness into pretrained 2D diffusion models, enhancing the robustness and 3D consistency of score distillation-based methods. We realize this by first constructing a coarse 3D structure of a given text prompt and then utilizing projected, view-specific depth map as a condition for the diffusion model. Additionally, we introduce a training strategy that enables the 2D diffusion model learns to handle the errors and sparsity within the coarse 3D structure for robust generation, as well as a method for ensuring semantic consistency throughout all viewpoints of the scene. Our framework surpasses the limitations of prior arts, and has significant implications for 3D consistent generation of 2D diffusion models.

Score Distillation Sampling (SDS) leverages pretrained 2D diffusion models to advance text-to-3D generation but neglects multi-view correlations, being prone to geometric inconsistencies and multi-face artifacts in the generated 3D content. In this work, we propose Coupled Score Distillation (CSD), a framework that couples multi-view joint distribution priors to ensure geometrically consistent 3D generation while enabling the stable and direct optimization of 3D Gaussian Splatting. Specifically, by reformulating the optimization as a multi-view joint optimization problem, we derive an effective optimization rule that effectively couples multi-view priors to guide optimization across different viewpoints while preserving the diversity of generated 3D assets. Additionally, we propose a framework that directly optimizes 3D Gaussian Splatting (3D-GS) with random initialization to generate geometrically consistent 3D content. We further employ a deformable tetrahedral grid, initialized from 3D-GS and refined through CSD, to produce high-quality, refined meshes. Quantitative and qualitative experimental results demonstrate the efficiency and competitive quality of our approach.

The recent advancements in text-to-3D generation mark a significant milestone in generative models, unlocking new possibilities for creating imaginative 3D assets across various real-world scenarios. While recent advancements in text-to-3D generation have shown promise, they often fall short in rendering detailed and high-quality 3D models. This problem is especially prevalent as many methods base themselves on Score Distillation Sampling (SDS). This paper identifies a notable deficiency in SDS, that it brings inconsistent and low-quality updating direction for the 3D model, causing the over-smoothing effect. To address this, we propose a novel approach called Interval Score Matching (ISM). ISM employs deterministic diffusing trajectories and utilizes interval-based score matching to counteract over-smoothing. Furthermore, we incorporate 3D Gaussian Splatting into our text-to-3D generation pipeline. Extensive experiments show that our model largely outperforms the state-of-the-art in quality and training efficiency.

Recent methods such as Score Distillation Sampling (SDS) and Variational Score Distillation (VSD) using 2D diffusion models for text-to-3D generation have demonstrated impressive generation quality. However, the long generation time of such algorithms significantly degrades the user experience. To tackle this problem, we propose DreamPropeller, a drop-in acceleration algorithm that can be wrapped around any existing text-to-3D generation pipeline based on score distillation. Our framework generalizes Picard iterations, a classical algorithm for parallel sampling an ODE path, and can account for non-ODE paths such as momentum-based gradient updates and changes in dimensions during the optimization process as in many cases of 3D generation. We show that our algorithm trades parallel compute for wallclock time and empirically achieves up to 4.7x speedup with a negligible drop in generation quality for all tested frameworks.

Score Distillation Sampling (SDS) has exhibited remarkable performance in conditional 3D content generation. However, a comprehensive understanding of the SDS formulation is still lacking, hindering the development of 3D generation. In this work, we present an interpretation of SDS as a combination of three functional components: mode-disengaging, mode-seeking and variance-reducing terms, and analyze the properties of each. We show that problems such as over-smoothness and color-saturation result from the intrinsic deficiency of the supervision terms and reveal that the variance-reducing term introduced by SDS is sub-optimal. Additionally, we shed light on the adoption of large Classifier-Free Guidance (CFG) scale for 3D generation. Based on the analysis, we propose a simple yet effective approach named Stable Score Distillation (SSD) which strategically orchestrates each term for high-quality 3D generation. Extensive experiments validate the efficacy of our approach, demonstrating its ability to generate high-fidelity 3D content without succumbing to issues such as over-smoothness and over-saturation, even under low CFG conditions with the most challenging NeRF representation.

We introduce Audio-SDS, a generalization of Score Distillation Sampling (SDS) to text-conditioned audio diffusion models. While SDS was initially designed for text-to-3D generation using image diffusion, its core idea of distilling a powerful generative prior into a separate parametric representation extends to the audio domain. Leveraging a single pretrained model, Audio-SDS enables a broad range of tasks without requiring specialized datasets. In particular, we demonstrate how Audio-SDS can guide physically informed impact sound simulations, calibrate FM-synthesis parameters, and perform prompt-specified source separation. Our findings illustrate the versatility of distillation-based methods across modalities and establish a robust foundation for future work using generative priors in audio tasks.

Although recent advancements in text-to-3D generation have significantly improved generation quality, issues like limited level of detail and low fidelity still persist, which requires further improvement. To understand the essence of those issues, we thoroughly analyze current score distillation methods by connecting theories of consistency distillation to score distillation. Based on the insights acquired through analysis, we propose an optimization framework, Guided Consistency Sampling (GCS), integrated with 3D Gaussian Splatting (3DGS) to alleviate those issues. Additionally, we have observed the persistent oversaturation in the rendered views of generated 3D assets. From experiments, we find that it is caused by unwanted accumulated brightness in 3DGS during optimization. To mitigate this issue, we introduce a Brightness-Equalized Generation (BEG) scheme in 3DGS rendering. Experimental results demonstrate that our approach generates 3D assets with more details and higher fidelity than state-of-the-art methods. The codes are released at https://github.com/LMozart/ECCV2024-GCS-BEG.

Real-time score following from sheet images remains chal- lenging because the model must process streaming au- dio while resolving highly repetitive visual patterns un- der strict latency constraints. Recent image-based meth- ods have attempted to use multi-resolution prediction by simultaneously predicting the positions of the active sys- tem, bar, and note. However, their predictions across these different levels of notation are independent, which makes the predictions unstable and introduces unnecessary ex- tra search space for bar- and note-level predictions. Most existing methods also lack mechanisms to recover from score discontinuities, such as repeats, da capo (D.C.), or coda jumps. This paper proposes CODA, to the best of our knowledge, the first real-time score following system that addresses both gaps. CODA explicitly exploits the cascaded structure of music scores: it first selects the ac- tive system, then the active bar within it, and finally the active note within the selected bar. This enforces pre- diction consistency across resolutions. A silence-driven break mode enables recovery from arbitrary score discon- tinuities without requiring knowledge of the repeat struc- ture. Evaluated on the Multimodal Sheet Music Dataset (MSMD) piano benchmarks, CODA achieves state-of-the- art tracking accuracy and discontinuity-recovery perfor- mance under real-time throughput. Code is available at https://github.com/ValleyC/CODA.

Existing Score Distillation Sampling (SDS)-based methods have driven significant progress in text-to-3D generation. However, 3D models produced by SDS-based methods tend to exhibit over-smoothing and low-quality outputs. These issues arise from the mode-seeking behavior of current methods, where the scores used to update the model oscillate between multiple modes, resulting in unstable optimization and diminished output quality. To address this problem, we introduce a novel image prompt score distillation loss named ISD, which employs a reference image to direct text-to-3D optimization toward a specific mode. Our ISD loss can be implemented by using IP-Adapter, a lightweight adapter for integrating image prompt capability to a text-to-image diffusion model, as a mode-selection module. A variant of this adapter, when not being prompted by a reference image, can serve as an efficient control variate to reduce variance in score estimates, thereby enhancing both output quality and optimization stability. Our experiments demonstrate that the ISD loss consistently achieves visually coherent, high-quality outputs and improves optimization speed compared to prior text-to-3D methods, as demonstrated through both qualitative and quantitative evaluations on the T3Bench benchmark suite.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Recently, text-to-3D generation has attracted significant attention, resulting in notable performance enhancements. Previous methods utilize end-to-end 3D generation models to initialize 3D Gaussians, multi-view diffusion models to enforce multi-view consistency, and text-to-image diffusion models to refine details with score distillation algorithms. However, these methods exhibit two limitations. Firstly, they encounter conflicts in generation directions since different models aim to produce diverse 3D assets. Secondly, the issue of over-saturation in score distillation has not been thoroughly investigated and solved. To address these limitations, we propose PlacidDreamer, a text-to-3D framework that harmonizes initialization, multi-view generation, and text-conditioned generation with a single multi-view diffusion model, while simultaneously employing a novel score distillation algorithm to achieve balanced saturation. To unify the generation direction, we introduce the Latent-Plane module, a training-friendly plug-in extension that enables multi-view diffusion models to provide fast geometry reconstruction for initialization and enhanced multi-view images to personalize the text-to-image diffusion model. To address the over-saturation problem, we propose to view score distillation as a multi-objective optimization problem and introduce the Balanced Score Distillation algorithm, which offers a Pareto Optimal solution that achieves both rich details and balanced saturation. Extensive experiments validate the outstanding capabilities of our PlacidDreamer. The code is available at https://github.com/HansenHuang0823/PlacidDreamer.

Diffusion distillation has emerged as a promising strategy for accelerating text-to-image (T2I) diffusion models by distilling a pretrained score network into a one- or few-step generator. While existing methods have made notable progress, they often rely on real or teacher-synthesized images to perform well when distilling high-resolution T2I diffusion models such as Stable Diffusion XL (SDXL), and their use of classifier-free guidance (CFG) introduces a persistent trade-off between text-image alignment and generation diversity. We address these challenges by optimizing Score identity Distillation (SiD) -- a data-free, one-step distillation framework -- for few-step generation. Backed by theoretical analysis that justifies matching a uniform mixture of outputs from all generation steps to the data distribution, our few-step distillation algorithm avoids step-specific networks and integrates seamlessly into existing pipelines, achieving state-of-the-art performance on SDXL at 1024x1024 resolution. To mitigate the alignment-diversity trade-off when real text-image pairs are available, we introduce a Diffusion GAN-based adversarial loss applied to the uniform mixture and propose two new guidance strategies: Zero-CFG, which disables CFG in the teacher and removes text conditioning in the fake score network, and Anti-CFG, which applies negative CFG in the fake score network. This flexible setup improves diversity without sacrificing alignment. Comprehensive experiments on SD1.5 and SDXL demonstrate state-of-the-art performance in both one-step and few-step generation settings, along with robustness to the absence of real images. Our efficient PyTorch implementation, along with the resulting one- and few-step distilled generators, will be released publicly as a separate branch at https://github.com/mingyuanzhou/SiD-LSG.

Diffusion models have shown remarkable performance in generation problems over various domains including images, videos, text, and audio. A practical bottleneck of diffusion models is their sampling speed, due to the repeated evaluation of score estimation networks during the inference. In this work, we propose a novel framework capable of adaptively allocating compute required for the score estimation, thereby reducing the overall sampling time of diffusion models. We observe that the amount of computation required for the score estimation may vary along the time step for which the score is estimated. Based on this observation, we propose an early-exiting scheme, where we skip the subset of parameters in the score estimation network during the inference, based on a time-dependent exit schedule. Using the diffusion models for image synthesis, we show that our method could significantly improve the sampling throughput of the diffusion models without compromising image quality. Furthermore, we also demonstrate that our method seamlessly integrates with various types of solvers for faster sampling, capitalizing on their compatibility to enhance overall efficiency. The source code and our experiments are available at https://github.com/taehong-moon/ee-diffusion

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.

Score Distillation Sampling (SDS) has emerged as a prevalent technique for text-to-3D generation, enabling 3D content creation by distilling view-dependent information from text-to-2D guidance. However, they frequently exhibit shortcomings such as over-saturated color and excess smoothness. In this paper, we conduct a thorough analysis of SDS and refine its formulation, finding that the core design is to model the distribution of rendered images. Following this insight, we introduce a novel strategy called Variational Distribution Mapping (VDM), which expedites the distribution modeling process by regarding the rendered images as instances of degradation from diffusion-based generation. This special design enables the efficient training of variational distribution by skipping the calculations of the Jacobians in the diffusion U-Net. We also introduce timestep-dependent Distribution Coefficient Annealing (DCA) to further improve distilling precision. Leveraging VDM and DCA, we use Gaussian Splatting as the 3D representation and build a text-to-3D generation framework. Extensive experiments and evaluations demonstrate the capability of VDM and DCA to generate high-fidelity and realistic assets with optimization efficiency.

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

Recent progress has shown promise in distilling multi-step video diffusion models into efficient few-step students. Among them, Distribution Matching Distillation (DMD) and its successor DMD2 achieved strong generation quality and fast convergence. However, due to the nature of the reverse Kullback--Leibler (KL) objective, these methods exhibit two persistent failure modes: a substantial drop in sample diversity, and visibly over-saturated outputs that deviate from real-video appearance. In this work, we propose Data-Forcing Distillation (DFD), a simple post-training framework that restores diversity and fidelity in DMD with only a single-line of code change. At its core is the teacher score discrepancy to guide the student toward the real-data distribution, pulling it to missing modes (mitigating mode collapse) and away from problematic modes absent in real data (avoiding over-saturation). We provide an in-depth theoretical analysis of our framework and validate our approach on text-to-video, image-to-video, and autoregressive video generation. With only 100--300 steps of finetuning, DFD effectively restores diversity and fidelity on both Wan2.1-1.3B and Cosmos-Predict2.5-2B model, resolving the over-saturation artifacts with significantly better video dynamics and appearance, and even outperforms the teacher model.

Score Distillation Sampling (SDS) has emerged as a prominent method for text-to-3D generation by leveraging the strengths of 2D diffusion models. However, SDS is limited to generation tasks and lacks the capability to edit existing 3D assets. Conversely, variants of SDS that introduce editing capabilities often can not generate new 3D assets effectively. In this work, we observe that the processes of generation and editing within SDS and its variants have unified underlying gradient terms. Building on this insight, we propose Unified Distillation Sampling (UDS), a method that seamlessly integrates both the generation and editing of 3D assets. Essentially, UDS refines the gradient terms used in vanilla SDS methods, unifying them to support both tasks. Extensive experiments demonstrate that UDS not only outperforms baseline methods in generating 3D assets with richer details but also excels in editing tasks, thereby bridging the gap between 3D generation and editing. The code is available on: https://github.com/xingy038/UDS.

Music scores are written representations of music and contain rich information about musical components. The visual information on music scores includes notes, rests, staff lines, clefs, dynamics, and articulations. This visual information in music scores contains more semantic information than audio and symbolic representations of music. Previous music score datasets have limited sizes and are mainly designed for optical music recognition (OMR). There is a lack of research on creating a large-scale benchmark dataset for music modeling and generation. In this work, we propose MusicScore, a large-scale music score dataset collected and processed from the International Music Score Library Project (IMSLP). MusicScore consists of image-text pairs, where the image is a page of a music score and the text is the metadata of the music. The metadata of MusicScore is extracted from the general information section of the IMSLP pages. The metadata includes rich information about the composer, instrument, piece style, and genre of the music pieces. MusicScore is curated into small, medium, and large scales of 400, 14k, and 200k image-text pairs with varying diversity, respectively. We build a score generation system based on a UNet diffusion model to generate visually readable music scores conditioned on text descriptions to benchmark the MusicScore dataset for music score generation. MusicScore is released to the public at https://huggingface.co/datasets/ZheqiDAI/MusicScore.

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress all the time steps with the gradient backpropagated from the score network. In order to produce meaningful gradients for the generator, the score network is trained to simultaneously match the real data distribution and mismatch the fake data distribution. This model has the following advantages: 1) For sampling, it generates a fake image with only one step forward. 2) For training, it only needs 10 diffusion steps.3) Compared with consistency model, it is free of the ill-posed problem caused by consistency loss. On the popular CIFAR-10 dataset, our model outperforms Consistency Model and Denoising Score Matching, which demonstrates the potential of the framework. We further provide more examples on the MINIST and LSUN datasets. The code is available on GitHub.

Large language model (LLM) agents increasingly take actions (screening applicants, recommending credit, triaging patients), yet fairness for LLMs is still measured by grading answers. We introduce AgentFairBench, a cheap, reproducible, multi-domain benchmark for demographic disparity in the actions of LLM agents. Grounded in a companion framework, the Bias Conduction Framework (BCF, restated here), it spans three regulator-anchored domains: hiring, lending, and medical triage. Synthetic, demographic-neutral profiles are evaluated in counterfactual matched sets that vary only a name-coded race x gender signal (in the Bertrand Mullainathan tradition), under four agent scaffolds of increasing agency (direct, chain-of-thought, multi-agent deliberation, tool-augmented). A NumPy-only harness computes counterfactual flip rate, mean absolute score difference (MASD), action-rate disparity, and tool-invocation disparity, with bootstrap confidence intervals, paired tests, and false-discovery-rate control, for single-digit dollars per model. A live leaderboard with a held-out private split and a contamination canary admits external models by submission. Our pilot (864 decisions plus a test-retest replication) carries a methodological lesson: comparing a six-group score spread against a two-run noise difference overstates disparity by ~ 2.4X through statistic arity alone. Against an arity matched noise floor and an omnibus group test, claude haiku 4 5 shows no demographic effect above sampling noise (0 of 120 pairwise and 0 of 9 omnibus contrasts survive correction); a planted-bias test confirms the instrument detects disparity when present. The contribution is a sound, sensitive, adoption-ready instrument, the arity matched null methodology, and open artifacts to scale it. Code, data, and harness are released under open licenses, with an anonymized review artifact.

On-policy distillation (OPD) applies token-level teacher supervision to student-generated trajectories, but this supervision is not always reliable. Existing methods use local confidence or teacher-student agreement to weight, filter, or truncate the sampled trajectory. These signals do not directly determine whether the teacher can continue a student prefix to a correct answer, and trajectory-level interventions can conflate one rollout's unreliability with low expected training value of its prompt. We define prompt-level teacher continuation reliability R as the teacher's probability of reaching a correct answer from a student prefix, averaged over prefixes and trajectories induced by the current student. Oracle experiments show that high-R prompts yield larger OPD gains and that descending-R training outperforms random and ascending orders on a fixed prompt pool. Because estimating R requires many teacher continuations, we use the maximum ROUGE-5 F1 between one independent student rollout and verifier-correct same-prompt teacher trajectories. Across ten equal-frequency bins of this actual score, mean R rises monotonically, showing that the proxy separates coarse reliability levels. ReOrder-OPD sorts prompts by the proxy, then draws independent on-policy training trajectories for vanilla OPD. It improves every matched aggregate comparison across Qwen3 and Gemma4 mathematics settings and Qwen3 code settings. Gains in all six FiRe-OPD and ExOPD settings show that prompt ordering complements within-trajectory supervision.

Diffusion models have been applied to 3D LiDAR scene completion due to their strong training stability and high completion quality. However, the slow sampling speed limits the practical application of diffusion-based scene completion models since autonomous vehicles require an efficient perception of surrounding environments. This paper proposes a novel distillation method tailored for 3D LiDAR scene completion models, dubbed ScoreLiDAR, which achieves efficient yet high-quality scene completion. ScoreLiDAR enables the distilled model to sample in significantly fewer steps after distillation. To improve completion quality, we also introduce a novel Structural Loss, which encourages the distilled model to capture the geometric structure of the 3D LiDAR scene. The loss contains a scene-wise term constraining the holistic structure and a point-wise term constraining the key landmark points and their relative configuration. Extensive experiments demonstrate that ScoreLiDAR significantly accelerates the completion time from 30.55 to 5.37 seconds per frame (>5times) on SemanticKITTI and achieves superior performance compared to state-of-the-art 3D LiDAR scene completion models. Our code is publicly available at https://github.com/happyw1nd/ScoreLiDAR.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.

Diffusion models have emerged as the backbone of modern generative AI, powering advances in vision, language, audio and other modalities. Despite their success, they suffer from hallucinations, implausible samples that lie outside the support of true data distribution, which degrade reliability and trust. In this work, we first empirically confirm previously proposed hypothesis that score smoothness causes hallucinations in Image Generation diffusion models and provide a density-based perspective. We further formalize this notion by linking the hallucinations probability mass to lipschitz constant of the learned score function. Motivated by this, we introduce a Variance-Guided Score Modulation (VSM) strategy that controls the score Jacobian, in turn reducing score smoothness and better approximating the ground truth score that decreases hallucinations. Empirical results on synthetic and real-world datasets demonstrate that our approach reduces hallucinations (up to ~25%) while maintaining high fidelity and diversity, providing a principled step toward more reliable diffusion-based image generation. We also propose two benchmark datasets with extreme semantic variation for systematic hallucination evaluation. Code and Datasets are publicly available at https://github.com/bhosalems/VSM.

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.

Risk decision systems in fraud detection and credit scoring operate under structural label absence: ground truth arrives weeks to months after decisions are made. During this blind period, model performance may degrade silently, eroding the governance evidence that justifies automated decisions. Existing drift detection methods either require labels (supervised detectors) or detect statistical change without distinguishing harmful degradation from benign distributional evolution (unsupervised detectors). No existing framework integrates drift detection with governance evidence assessment and operational response. This paper presents a label-free governance monitoring extension to the Governance Drift Toolkit that produces governance alerts rather than statistical alarms. The monitoring architecture applies composite multi-proxy monitoring across four proxy monitors (score distribution, feature drift, prediction entropy, confidence distribution), with governance-calibrated thresholds. Empirical evaluation on the Lending Club credit scoring dataset (1.37M loans, 11 years) demonstrates three findings. First, raw proxy metrics (Feature PSI delta up to 1.84, Score PSI delta up to 0.92) distinguish injected covariate degradation from natural temporal drift in an offline evaluation setting. Second, pure concept drift in P(Y|X) produces exactly zero delta across all proxy metrics in all windows, confirming the irreducible blind spot of label-free monitoring as a structural verification. Third, the composite score provides monotonic severity progression as more monitors trigger (0.583 to 0.833 to 1.000), enabling graduated governance response. Cross-domain comparison with IEEE-CIS fraud detection results shows the detectable/undetectable boundary is consistent across both domains. The toolkit and evaluation code are available as open-source artifacts.

ICC's current ranking system does not adequately account for key contextual factors such as home advantage, toss impact and scheduling imbalances; leading to inconsistencies in team evaluation in Test cricket. This study develops an enhanced rating framework by adapting and enhancing Glicko's model to incorporate these influences alongside Margin of Victory, an important indicator of dominance a contest. This enables a more dynamic and probabilistically grounded assessment of team performance. Using past match data, the model demonstrates improved expected score estimation and predictive accuracy. Robustness of the resulting ratings is demonstrated through bootstrap resampling, confirming stability with respect to match scheduling. Overall, the framework provides a fairer and more statistically consistent approach to ranking Test teams.

Diffusion-based generative models have recently achieved remarkable results in speech and vocal enhancement due to their ability to model complex speech data distributions. While these models generalize well to unseen acoustic environments, they may not achieve the same level of fidelity as the discriminative models specifically trained to enhance particular acoustic conditions. In this paper, we propose Ex-Diff, a novel score-based diffusion model that integrates the latent representations produced by a discriminative model to improve speech and vocal enhancement, which combines the strengths of both generative and discriminative models. Experimental results on the widely used MUSDB dataset show relative improvements of 3.7% in SI-SDR and 10.0% in SI-SIR compared to the baseline diffusion model for speech and vocal enhancement tasks, respectively. Additionally, case studies are provided to further illustrate and analyze the complementary nature of generative and discriminative models in this context.

Large Language Model agents excel at solving complex tasks through iterative reasoning and tool use, but typically depend on ultra-large, costly backbones. Existing distillation approaches train smaller students to imitate full teacher trajectories, yet reasoning and knowledge gaps between the teacher and student often lead to compounding errors. We propose SCoRe, a student-centered framework in which the student generates trajectories and the teacher intervenes only at the first critical error, producing training data matched to the student's ability and exposing specific weaknesses. The student is first fine-tuned on corrected trajectories. Subsequently, short-horizon reinforcement learning starts from the verified prefix before the first critical error, with target rewards assigned at that step. This design encourages autonomous problem-solving beyond imitation and improves training stability. Particularly, on 12 challenging benchmarks, a 7B-parameter student distilled with SCoRe matches the agentic performance of a 72B-parameter teacher.

Diffusion probabilistic models have shown significant progress in video generation; however, their computational efficiency is limited by the large number of sampling steps required. Reducing sampling steps often compromises video quality or generation diversity. In this work, we introduce a distillation method that combines variational score distillation and consistency distillation to achieve few-step video generation, maintaining both high quality and diversity. We also propose a latent reward model fine-tuning approach to further enhance video generation performance according to any specified reward metric. This approach reduces memory usage and does not require the reward to be differentiable. Our method demonstrates state-of-the-art performance in few-step generation for 10-second videos (128 frames at 12 FPS). The distilled student model achieves a score of 82.57 on VBench, surpassing the teacher model as well as baseline models Gen-3, T2V-Turbo, and Kling. One-step distillation accelerates the teacher model's diffusion sampling by up to 278.6 times, enabling near real-time generation. Human evaluations further validate the superior performance of our 4-step student models compared to teacher model using 50-step DDIM sampling.

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved question: which score do they actually learn? In principle, a diffusion model that matches the empirical score in the entire data space would simply reproduce the training data, failing to generate novel samples. Recent work addresses this question by arguing that diffusion models underfit the empirical score due to training-time inductive biases. In this work, we refine this perspective, introducing the notion of selective underfitting: instead of underfitting the score everywhere, better diffusion models more accurately approximate the score in certain regions of input space, while underfitting it in others. We characterize these regions and design empirical interventions to validate our perspective. Our results establish that selective underfitting is essential for understanding diffusion models, yielding new, testable insights into their generalization and generative performance.

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

Despite the remarkable performance of score distillation in text-to-3D generation, such techniques notoriously suffer from view inconsistency issues, also known as "Janus" artifact, where the generated objects fake each view with multiple front faces. Although empirically effective methods have approached this problem via score debiasing or prompt engineering, a more rigorous perspective to explain and tackle this problem remains elusive. In this paper, we reveal that the existing score distillation-based text-to-3D generation frameworks degenerate to maximal likelihood seeking on each view independently and thus suffer from the mode collapse problem, manifesting as the Janus artifact in practice. To tame mode collapse, we improve score distillation by re-establishing in entropy term in the corresponding variational objective, which is applied to the distribution of rendered images. Maximizing the entropy encourages diversity among different views in generated 3D assets, thereby mitigating the Janus problem. Based on this new objective, we derive a new update rule for 3D score distillation, dubbed Entropic Score Distillation (ESD). We theoretically reveal that ESD can be simplified and implemented by just adopting the classifier-free guidance trick upon variational score distillation. Although embarrassingly straightforward, our extensive experiments successfully demonstrate that ESD can be an effective treatment for Janus artifacts in score distillation.

We introduce Adversarial Diffusion Distillation (ADD), a novel training approach that efficiently samples large-scale foundational image diffusion models in just 1-4 steps while maintaining high image quality. We use score distillation to leverage large-scale off-the-shelf image diffusion models as a teacher signal in combination with an adversarial loss to ensure high image fidelity even in the low-step regime of one or two sampling steps. Our analyses show that our model clearly outperforms existing few-step methods (GANs, Latent Consistency Models) in a single step and reaches the performance of state-of-the-art diffusion models (SDXL) in only four steps. ADD is the first method to unlock single-step, real-time image synthesis with foundation models. Code and weights available under https://github.com/Stability-AI/generative-models and https://huggingface.co/stabilityai/ .

Failure of machine learning models to generalize to new data is a core problem limiting the reliability of AI systems, partly due to the lack of simple and robust methods for comparing new data to the original training dataset. We propose a standardized approach for assessing data similarity in a model-agnostic manner by constructing a supervised autoencoder for generalizability estimation (SAGE). We compare points in a low-dimensional embedded latent space, defining empirical probability measures for k-Nearest Neighbors (kNN) distance, reconstruction of inputs and task-based performance. As proof of concept for classification tasks, we use MNIST and CIFAR-10 to demonstrate how an ensemble output probability score can separate deformed images from a mixture of typical test examples, and how this SAGE score is robust to transformations of increasing severity. As further proof of concept, we extend this approach to a regression task using non-imaging data (UCI Abalone). In all cases, we show that out-of-the-box model performance increases after SAGE score filtering, even when applied to data from the model's own training and test datasets. Our out-of-distribution scoring method can be introduced during several steps of model construction and assessment, leading to future improvements in responsible deep learning implementation.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

We introduce Delta Denoising Score (DDS), a novel scoring function for text-based image editing that guides minimal modifications of an input image towards the content described in a target prompt. DDS leverages the rich generative prior of text-to-image diffusion models and can be used as a loss term in an optimization problem to steer an image towards a desired direction dictated by a text. DDS utilizes the Score Distillation Sampling (SDS) mechanism for the purpose of image editing. We show that using only SDS often produces non-detailed and blurry outputs due to noisy gradients. To address this issue, DDS uses a prompt that matches the input image to identify and remove undesired erroneous directions of SDS. Our key premise is that SDS should be zero when calculated on pairs of matched prompts and images, meaning that if the score is non-zero, its gradients can be attributed to the erroneous component of SDS. Our analysis demonstrates the competence of DDS for text based image-to-image translation. We further show that DDS can be used to train an effective zero-shot image translation model. Experimental results indicate that DDS outperforms existing methods in terms of stability and quality, highlighting its potential for real-world applications in text-based image editing.

Automated Essay Score (AES) is proven to be one of the cutting-edge technologies. Scoring techniques are used for various purposes. Reliable scores are calculated based on influential variables. Such variables can be computed by different methods based on the domain. The research is concentrated on the user's understanding of a given topic. The analysis is based on a scoring index by using Large Language Models. The user can then compare and contrast the understanding of a topic that they recently learned. The results are then contributed towards learning analytics and progression is made for enhancing the learning ability. In this research, the focus is on summarizing a PDF document and gauging a user's understanding of its content. The process involves utilizing a Langchain tool to summarize the PDF and extract the essential information. By employing this technique, the research aims to determine how well the user comprehends the summarized content.

Diffusion models have achieved impressive results in generative tasks such as text-to-image synthesis, yet they often struggle to fully align outputs with nuanced user intent and maintain consistent aesthetic quality. Existing preference-based training methods like Diffusion Direct Preference Optimization help address these issues but rely on costly and potentially noisy human-labeled datasets. In this work, we introduce Direct Diffusion Score Preference Optimization (DDSPO), which directly derives per-timestep supervision from winning and losing policies when such policies are available. Unlike prior methods that operate solely on final samples, DDSPO provides dense, transition-level signals across the denoising trajectory. In practice, we avoid reliance on labeled data by automatically generating preference signals using a pretrained reference model: we contrast its outputs when conditioned on original prompts versus semantically degraded variants. This practical strategy enables effective score-space preference supervision without explicit reward modeling or manual annotations. Empirical results demonstrate that DDSPO improves text-image alignment and visual quality, outperforming or matching existing preference-based methods while requiring significantly less supervision. Our implementation is available at: https://dohyun-as.github.io/DDSPO

Score-based generative models, commonly referred to as diffusion models, have proven to be successful at generating text and image data. However, their adaptation to mixed-type tabular data remains underexplored. In this work, we propose CDTD, a Continuous Diffusion model for mixed-type Tabular Data. CDTD is based on a novel combination of score matching and score interpolation to enforce a unified continuous noise distribution for both continuous and categorical features. We explicitly acknowledge the necessity of homogenizing distinct data types by relying on model-specific loss calibration and initialization schemes.To further address the high heterogeneity in mixed-type tabular data, we introduce adaptive feature- or type-specific noise schedules. These ensure balanced generative performance across features and optimize the allocation of model capacity across features and diffusion time. Our experimental results show that CDTD consistently outperforms state-of-the-art benchmark models, captures feature correlations exceptionally well, and that heterogeneity in the noise schedule design boosts sample quality. Replication code is available at https://github.com/muellermarkus/cdtd.

The application of diffusion models in 3D LiDAR scene completion is limited due to diffusion's slow sampling speed. Score distillation accelerates diffusion sampling but with performance degradation, while post-training with direct policy optimization (DPO) boosts performance using preference data. This paper proposes Distillation-DPO, a novel diffusion distillation framework for LiDAR scene completion with preference aligment. First, the student model generates paired completion scenes with different initial noises. Second, using LiDAR scene evaluation metrics as preference, we construct winning and losing sample pairs. Such construction is reasonable, since most LiDAR scene metrics are informative but non-differentiable to be optimized directly. Third, Distillation-DPO optimizes the student model by exploiting the difference in score functions between the teacher and student models on the paired completion scenes. Such procedure is repeated until convergence. Extensive experiments demonstrate that, compared to state-of-the-art LiDAR scene completion diffusion models, Distillation-DPO achieves higher-quality scene completion while accelerating the completion speed by more than 5-fold. Our method is the first to explore adopting preference learning in distillation to the best of our knowledge and provide insights into preference-aligned distillation. Our code is public available on https://github.com/happyw1nd/DistillationDPO.

Reward models are central to text-to-image post-training, but visual preference is subjective and better represented as a distribution over rubric scores than as a deterministic scalar. Existing scalar, score-token, and pairwise reward models over-compress uncertainty and fine-grained score differences, while reasoning-based generative rewards provide stronger judgments but are costly to deploy and difficult to use as direct optimization signals. We propose Z-Reward, a teacher-student reward modeling framework that decouples reasoning-heavy judgment from efficient reward deployment. The teacher is a large VLM that uses reasoning to infer rubric-aligned score distributions, and is trained with Group-wise Direct Score Optimization (GDSO), which combines policy-gradient rewards from distribution expectations with direct pointwise and pairwise supervision on score distributions and score gaps. The student is trained with Reasoning-Internalized Score Distillation (RISD), which transfers the teacher's reasoning-conditioned score distribution into a compact VLM without requiring explicit reasoning chains at inference time. On our internally annotated evaluation set, the 27B GDSO teacher reaches 89.6% human preference accuracy, outperforming SFT, RewardDance, and GRPO, while the 9B RISD student reaches 88.6%, outperforming the OPD baseline and closely matching the larger teacher. We further show that Z-Reward can serve as a differentiable reward signal for text-to-image optimization, yielding a 41.3% net human-preference improvement over the SFT baseline.

In this paper we show that reporting a single performance score is insufficient to compare non-deterministic approaches. We demonstrate for common sequence tagging tasks that the seed value for the random number generator can result in statistically significant (p < 10^-4) differences for state-of-the-art systems. For two recent systems for NER, we observe an absolute difference of one percentage point F1-score depending on the selected seed value, making these systems perceived either as state-of-the-art or mediocre. Instead of publishing and reporting single performance scores, we propose to compare score distributions based on multiple executions. Based on the evaluation of 50.000 LSTM-networks for five sequence tagging tasks, we present network architectures that produce both superior performance as well as are more stable with respect to the remaining hyperparameters.

Despite their strong performances on many generative tasks, diffusion models require a large number of sampling steps in order to generate realistic samples. This has motivated the community to develop effective methods to distill pre-trained diffusion models into more efficient models, but these methods still typically require few-step inference or perform substantially worse than the underlying model. In this paper, we present Score Implicit Matching (SIM) a new approach to distilling pre-trained diffusion models into single-step generator models, while maintaining almost the same sample generation ability as the original model as well as being data-free with no need of training samples for distillation. The method rests upon the fact that, although the traditional score-based loss is intractable to minimize for generator models, under certain conditions we can efficiently compute the gradients for a wide class of score-based divergences between a diffusion model and a generator. SIM shows strong empirical performances for one-step generators: on the CIFAR10 dataset, it achieves an FID of 2.06 for unconditional generation and 1.96 for class-conditional generation. Moreover, by applying SIM to a leading transformer-based diffusion model, we distill a single-step generator for text-to-image (T2I) generation that attains an aesthetic score of 6.42 with no performance decline over the original multi-step counterpart, clearly outperforming the other one-step generators including SDXL-TURBO of 5.33, SDXL-LIGHTNING of 5.34 and HYPER-SDXL of 5.85. We will release this industry-ready one-step transformer-based T2I generator along with this paper.

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion models for Imputation (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Unlike existing score-based approaches, the conditional diffusion model is explicitly trained for imputation and can exploit correlations between observed values. On healthcare and environmental data, CSDI improves by 40-65% over existing probabilistic imputation methods on popular performance metrics. In addition, deterministic imputation by CSDI reduces the error by 5-20% compared to the state-of-the-art deterministic imputation methods. Furthermore, CSDI can also be applied to time series interpolation and probabilistic forecasting, and is competitive with existing baselines. The code is available at https://github.com/ermongroup/CSDI.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Generative priors of large-scale text-to-image diffusion models enable a wide range of new generation and editing applications on diverse visual modalities. However, when adapting these priors to complex visual modalities, often represented as multiple images (e.g., video), achieving consistency across a set of images is challenging. In this paper, we address this challenge with a novel method, Collaborative Score Distillation (CSD). CSD is based on the Stein Variational Gradient Descent (SVGD). Specifically, we propose to consider multiple samples as "particles" in the SVGD update and combine their score functions to distill generative priors over a set of images synchronously. Thus, CSD facilitates seamless integration of information across 2D images, leading to a consistent visual synthesis across multiple samples. We show the effectiveness of CSD in a variety of tasks, encompassing the visual editing of panorama images, videos, and 3D scenes. Our results underline the competency of CSD as a versatile method for enhancing inter-sample consistency, thereby broadening the applicability of text-to-image diffusion models.

Despite advances in diffusion-based text-to-music (TTM) methods, efficient, high-quality generation remains a challenge. We introduce Presto!, an approach to inference acceleration for score-based diffusion transformers via reducing both sampling steps and cost per step. To reduce steps, we develop a new score-based distribution matching distillation (DMD) method for the EDM-family of diffusion models, the first GAN-based distillation method for TTM. To reduce the cost per step, we develop a simple, but powerful improvement to a recent layer distillation method that improves learning via better preserving hidden state variance. Finally, we combine our step and layer distillation methods together for a dual-faceted approach. We evaluate our step and layer distillation methods independently and show each yield best-in-class performance. Our combined distillation method can generate high-quality outputs with improved diversity, accelerating our base model by 10-18x (230/435ms latency for 32 second mono/stereo 44.1kHz, 15x faster than comparable SOTA) -- the fastest high-quality TTM to our knowledge. Sound examples can be found at https://presto-music.github.io/web/.

Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical distributions in this work. Next, we examine an alternative view: we consider the denoising posterior P(X|Y) as the optimizer of the energy score (a scoring rule) and derive a fundamental identity that connects the (path-) derivative of a (possibly) non-Euclidean energy score to the score of the noisy marginal. This identity can be seen as an analog of Tweedie's identity for the energy score, and allows for several interesting applications; for example, score estimation, noise distribution parameter estimation, as well as using energy score models in the context of "traditional" diffusion model samplers with a wider array of noising distributions.

This work represents the first effort to scale up continuous-time consistency distillation to general application-level image and video diffusion models. Although continuous-time consistency model (sCM) is theoretically principled and empirically powerful for accelerating academic-scale diffusion, its applicability to large-scale text-to-image and video tasks remains unclear due to infrastructure challenges in Jacobian-vector product (JVP) computation and the limitations of standard evaluation benchmarks. We first develop a parallelism-compatible FlashAttention-2 JVP kernel, enabling sCM training on models with over 10 billion parameters and high-dimensional video tasks. Our investigation reveals fundamental quality limitations of sCM in fine-detail generation, which we attribute to error accumulation and the "mode-covering" nature of its forward-divergence objective. To remedy this, we propose the score-regularized continuous-time consistency model (rCM), which incorporates score distillation as a long-skip regularizer. This integration complements sCM with the "mode-seeking" reverse divergence, effectively improving visual quality while maintaining high generation diversity. Validated on large-scale models (Cosmos-Predict2, Wan2.1) up to 14B parameters and 5-second videos, rCM matches or surpasses the state-of-the-art distillation method DMD2 on quality metrics while offering notable advantages in diversity, all without GAN tuning or extensive hyperparameter searches. The distilled models generate high-fidelity samples in only 1sim4 steps, accelerating diffusion sampling by 15timessim50times. These results position rCM as a practical and theoretically grounded framework for advancing large-scale diffusion distillation.

Consistency models are a nascent family of generative models that can sample high quality data in one step without the need for adversarial training. Current consistency models achieve optimal sample quality by distilling from pre-trained diffusion models and employing learned metrics such as LPIPS. However, distillation limits the quality of consistency models to that of the pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation. To tackle these challenges, we present improved techniques for consistency training, where consistency models learn directly from data without distillation. We delve into the theory behind consistency training and identify a previously overlooked flaw, which we address by eliminating Exponential Moving Average from the teacher consistency model. To replace learned metrics like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally, we introduce a lognormal noise schedule for the consistency training objective, and propose to double total discretization steps every set number of training iterations. Combined with better hyperparameter tuning, these modifications enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10 and ImageNet 64times 64 respectively in a single sampling step. These scores mark a 3.5times and 4times improvement compared to prior consistency training approaches. Through two-step sampling, we further reduce FID scores to 2.24 and 2.77 on these two datasets, surpassing those obtained via distillation in both one-step and two-step settings, while narrowing the gap between consistency models and other state-of-the-art generative models.

Visual artifacts remain a persistent challenge in diffusion models, even with training on massive datasets. Current solutions primarily rely on supervised detectors, yet lack understanding of why these artifacts occur in the first place. In our analysis, we identify three distinct phases in the diffusion generative process: Profiling, Mutation, and Refinement. Artifacts typically emerge during the Mutation phase, where certain regions exhibit anomalous score dynamics over time, causing abrupt disruptions in the normal evolution pattern. This temporal nature explains why existing methods focusing only on spatial uncertainty of the final output fail at effective artifact localization. Based on these insights, we propose ASCED (Abnormal Score Correction for Enhancing Diffusion), that detects artifacts by monitoring abnormal score dynamics during the diffusion process, with a trajectory-aware on-the-fly mitigation strategy that appropriate generation of noise in the detected areas. Unlike most existing methods that apply post hoc corrections, \eg, by applying a noising-denoising scheme after generation, our mitigation strategy operates seamlessly within the existing diffusion process. Extensive experiments demonstrate that our proposed approach effectively reduces artifacts across diverse domains, matching or surpassing existing supervised methods without additional training.

Sampling from diffusion models involves a slow iterative process that hinders their practical deployment, especially for interactive applications. To accelerate generation speed, recent approaches distill a multi-step diffusion model into a single-step student generator via variational score distillation, which matches the distribution of samples generated by the student to the teacher's distribution. However, these approaches use the reverse Kullback-Leibler (KL) divergence for distribution matching which is known to be mode seeking. In this paper, we generalize the distribution matching approach using a novel f-divergence minimization framework, termed f-distill, that covers different divergences with different trade-offs in terms of mode coverage and training variance. We derive the gradient of the f-divergence between the teacher and student distributions and show that it is expressed as the product of their score differences and a weighting function determined by their density ratio. This weighting function naturally emphasizes samples with higher density in the teacher distribution, when using a less mode-seeking divergence. We observe that the popular variational score distillation approach using the reverse-KL divergence is a special case within our framework. Empirically, we demonstrate that alternative f-divergences, such as forward-KL and Jensen-Shannon divergences, outperform the current best variational score distillation methods across image generation tasks. In particular, when using Jensen-Shannon divergence, f-distill achieves current state-of-the-art one-step generation performance on ImageNet64 and zero-shot text-to-image generation on MS-COCO. Project page: https://research.nvidia.com/labs/genair/f-distill

Recent advances in one-step generative models typically follow a two-stage process: first training a teacher diffusion model and then distilling it into a one-step student model. This distillation process traditionally relies on both the teacher model's score function to compute the distillation loss and its weights for student initialization. In this paper, we explore whether one-step generative models can be trained directly without this distillation process. First, we show that the teacher's score function is not essential and propose a family of distillation methods that achieve competitive results without relying on score estimation. Next, we demonstrate that initialization from teacher weights is indispensable in successful training. Surprisingly, we find that this benefit is not due to improved ``input-output" mapping but rather the learned feature representations, which dominate distillation quality. Our findings provide a better understanding of the role of initialization in one-step model training and its impact on distillation quality.

Despite the potential of diffusion models in speech enhancement, their deployment in Acoustic Echo Cancellation (AEC) has been restricted. In this paper, we propose DI-AEC, pioneering a diffusion-based stochastic regeneration approach dedicated to AEC. Further, we propose FADI-AEC, fast score-based diffusion AEC framework to save computational demands, making it favorable for edge devices. It stands out by running the score model once per frame, achieving a significant surge in processing efficiency. Apart from that, we introduce a novel noise generation technique where far-end signals are utilized, incorporating both far-end and near-end signals to refine the score model's accuracy. We test our proposed method on the ICASSP2023 Microsoft deep echo cancellation challenge evaluation dataset, where our method outperforms some of the end-to-end methods and other diffusion based echo cancellation methods.

The development of diffusion-based generative models over the past decade has largely proceeded independently of progress in representation learning. These diffusion models typically rely on regression-based objectives and generally lack explicit regularization. In this work, we propose Dispersive Loss, a simple plug-and-play regularizer that effectively improves diffusion-based generative models. Our loss function encourages internal representations to disperse in the hidden space, analogous to contrastive self-supervised learning, with the key distinction that it requires no positive sample pairs and therefore does not interfere with the sampling process used for regression. Compared to the recent method of representation alignment (REPA), our approach is self-contained and minimalist, requiring no pre-training, no additional parameters, and no external data. We evaluate Dispersive Loss on the ImageNet dataset across a range of models and report consistent improvements over widely used and strong baselines. We hope our work will help bridge the gap between generative modeling and representation learning.

GossipSub is a popular new peer-to-peer network protocol designed to disseminate messages quickly and efficiently by allowing peers to forward the full content of messages only to a dynamically selected subset of their neighboring peers (mesh neighbors) while gossiping about messages they have seen with the rest. Peers decide which of their neighbors to graft or prune from their mesh locally and periodically using a score for each neighbor. Scores are calculated using a score function that depends on mesh-specific parameters, weights and counters relating to a peer's performance in the network. Since a GossipSub network's performance ultimately depends on the performance of its peers, an important question arises: Is the score calculation mechanism effective in weeding out non-performing or even intentionally misbehaving peers from meshes? We answered this question in the negative in our companion paper by reasoning about GossipSub using our formal, official and executable ACL2s model. Based on our findings, we synthesized and simulated attacks against GossipSub which were confirmed by the developers of GossipSub, FileCoin, and Eth2.0, and publicly disclosed in MITRE CVE-2022-47547. In this paper, we present a detailed description of our model. We discuss design decisions, security properties of GossipSub, reasoning about the security properties in context of our model, attack generation and lessons we learnt when writing it.

Real-world data deviating from the independent and identically distributed (i.i.d.) assumption of in-distribution training data poses security threats to deep networks, thus advancing out-of-distribution (OOD) detection algorithms. Detection methods in generative language models (GLMs) mainly focus on uncertainty estimation and embedding distance measurement, with the latter proven to be most effective in traditional linguistic tasks like summarization and translation. However, another complex generative scenario mathematical reasoning poses significant challenges to embedding-based methods due to its high-density feature of output spaces, but this feature causes larger discrepancies in the embedding shift trajectory between different samples in latent spaces. Hence, we propose a trajectory-based method TV score, which uses trajectory volatility for OOD detection in mathematical reasoning. Experiments show that our method outperforms all traditional algorithms on GLMs under mathematical reasoning scenarios and can be extended to more applications with high-density features in output spaces, such as multiple-choice questions.

Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from the neural network backbone learning a smoothed version of the empirical score function, which guides the denoising dynamics to generate data points that interpolate the training data. Focusing mainly on settings where the training set lies uniformly in a one-dimensional subspace, we elucidate the interplay between score smoothing and the denoising dynamics with analytical solutions and numerical experiments, demonstrating how smoothing the score function can cause the denoised data samples to interpolate the training set along the subspace. Moreover, we present theoretical and empirical evidence that learning score functions with neural networks - either with or without explicit regularization - can naturally achieve a similar effect, including when the data belong to simple nonlinear manifolds.

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt Mixer, is tested on the AIMO 3 competition: 3 models, 23+ experiments, 50 IMO-level problems, one H100 80 GB, 5-hour limit. Every prompt-level intervention fails. High-temperature sampling already decorrelates errors; weaker strategies reduce accuracy more than they reduce correlation. Across an 8-point capability gap at equal N=8 and every optimization tested, model capability dominates. The gap between the best majority-vote score (42/50) and pass@20 (~45.5) is selection loss, not prompt loss. A verifier-based selector could close it. Prompt engineering cannot.

Individual user fairness is commonly understood as treating similar users similarly. In Recommender Systems (RSs), several evaluation measures exist for quantifying individual user fairness. These measures evaluate fairness via either: (i) the disparity in RS effectiveness scores regardless of user similarity, or (ii) the disparity in items recommended to similar users regardless of item relevance. Both disparity in recommendation effectiveness and user similarity are very important in fairness, yet no existing individual user fairness measure simultaneously accounts for both. In brief, current user fairness evaluation measures implement a largely incomplete definition of fairness. To fill this gap, we present Pairwise User unFairness (PUF), a novel evaluation measure of individual user fairness that considers both effectiveness disparity and user similarity. PUF is the only measure that can express this important distinction. We empirically validate that PUF does this consistently across 4 datasets and 7 rankers, and robustly when varying user similarity or effectiveness. In contrast, all other measures are either almost insensitive to effectiveness disparity or completely insensitive to user similarity. We contribute the first RS evaluation measure to reliably capture both user similarity and effectiveness in individual user fairness. Our code: https://github.com/theresiavr/PUF-individual-user-fairness-recsys.

Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find that its distillation sampling process indeed corresponds to the trajectory sampling of a stochastic differential equation (SDE): SDS samples along an SDE trajectory to yield a less noisy sample which then serves as a guidance to optimize a 3D model. However, the randomness in SDE sampling often leads to a diverse and unpredictable sample which is not always less noisy, and thus is not a consistently correct guidance, explaining the vulnerability of SDS. Since for any SDE, there always exists an ordinary differential equation (ODE) whose trajectory sampling can deterministically and consistently converge to the desired target point as the SDE, we propose a novel and effective "Consistent3D" method that explores the ODE deterministic sampling prior for text-to-3D generation. Specifically, at each training iteration, given a rendered image by a 3D model, we first estimate its desired 3D score function by a pre-trained 2D diffusion model, and build an ODE for trajectory sampling. Next, we design a consistency distillation sampling loss which samples along the ODE trajectory to generate two adjacent samples and uses the less noisy sample to guide another more noisy one for distilling the deterministic prior into the 3D model. Experimental results show the efficacy of our Consistent3D in generating high-fidelity and diverse 3D objects and large-scale scenes, as shown in Fig. 1. The codes are available at https://github.com/sail-sg/Consistent3D.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

In recent years, advancements in generative models have significantly expanded the capabilities of text-to-3D generation. Many approaches rely on Score Distillation Sampling (SDS) technology. However, SDS struggles to accommodate multi-condition inputs, such as text and visual prompts, in customized generation tasks. To explore the core reasons, we decompose SDS into a difference term and a classifier-free guidance term. Our analysis identifies the core issue as arising from the difference term and the random noise addition during the optimization process, both contributing to deviations from the target mode during distillation. To address this, we propose a novel algorithm, Classifier Score Matching (CSM), which removes the difference term in SDS and uses a deterministic noise addition process to reduce noise during optimization, effectively overcoming the low-quality limitations of SDS in our customized generation framework. Based on CSM, we integrate visual prompt information with an attention fusion mechanism and sampling guidance techniques, forming the Visual Prompt CSM (VPCSM) algorithm. Furthermore, we introduce a Semantic-Geometry Calibration (SGC) module to enhance quality through improved textual information integration. We present our approach as TV-3DG, with extensive experiments demonstrating its capability to achieve stable, high-quality, customized 3D generation. Project page: https://yjhboy.github.io/TV-3DG

Controllable music generation methods are critical for human-centered AI-based music creation, but are currently limited by speed, quality, and control design trade-offs. Diffusion Inference-Time T-optimization (DITTO), in particular, offers state-of-the-art results, but is over 10x slower than real-time, limiting practical use. We propose Distilled Diffusion Inference-Time T -Optimization (or DITTO-2), a new method to speed up inference-time optimization-based control and unlock faster-than-real-time generation for a wide-variety of applications such as music inpainting, outpainting, intensity, melody, and musical structure control. Our method works by (1) distilling a pre-trained diffusion model for fast sampling via an efficient, modified consistency or consistency trajectory distillation process (2) performing inference-time optimization using our distilled model with one-step sampling as an efficient surrogate optimization task and (3) running a final multi-step sampling generation (decoding) using our estimated noise latents for best-quality, fast, controllable generation. Through thorough evaluation, we find our method not only speeds up generation over 10-20x, but simultaneously improves control adherence and generation quality all at once. Furthermore, we apply our approach to a new application of maximizing text adherence (CLAP score) and show we can convert an unconditional diffusion model without text inputs into a model that yields state-of-the-art text control. Sound examples can be found at https://ditto-music.github.io/ditto2/.

We propose FlowDec, a neural full-band audio codec for general audio sampled at 48 kHz that combines non-adversarial codec training with a stochastic postfilter based on a novel conditional flow matching method. Compared to the prior work ScoreDec which is based on score matching, we generalize from speech to general audio and move from 24 kbit/s to as low as 4 kbit/s, while improving output quality and reducing the required postfilter DNN evaluations from 60 to 6 without any fine-tuning or distillation techniques. We provide theoretical insights and geometric intuitions for our approach in comparison to ScoreDec as well as another recent work that uses flow matching, and conduct ablation studies on our proposed components. We show that FlowDec is a competitive alternative to the recent GAN-dominated stream of neural codecs, achieving FAD scores better than those of the established GAN-based codec DAC and listening test scores that are on par, and producing qualitatively more natural reconstructions for speech and harmonic structures in music.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.

Diffusion distillation, exemplified by Distribution Matching Distillation (DMD), has shown great promise in few-step generation but often sacrifices quality for sampling speed. While integrating Reinforcement Learning (RL) into distillation offers potential, a naive fusion of these two objectives relies on suboptimal raw sample evaluation. This sample-based scoring creates inherent conflicts with the distillation trajectory and produces unreliable rewards due to the noisy nature of early-stage generation. To overcome these limitations, we propose GDMD, a novel framework that redefines the reward mechanism by prioritizing distillation gradients over raw pixel outputs as the primary signal for optimization. By reinterpreting the DMD gradients as implicit target tensors, our framework enables existing reward models to directly evaluate the quality of distillation updates. This gradient-level guidance functions as an adaptive weighting that synchronizes the RL policy with the distillation objective, effectively neutralizing optimization divergence. Empirical results show that GDMD sets a new SOTA for few-step generation. Specifically, our 4-step models outperform the quality of their multi-step teacher and substantially exceed previous DMDR results in GenEval and human-preference metrics, exhibiting strong scalability potential.

Text and lyrics specify broad musical characteristics and sung content but offer limited control over musical timing, melody, and reference-based style. We introduce DiffSynth-Music (https://modelscope.cn/models/DiffSynth-Studio/DiffSynth-Music), a framework that adds composable audio conditioning to a music synthesis backbone through layer-wise key-value injection. The three template models, Control, Prosody, and Reference, are initialized from the backbone diffusion transformer and trained with conditional flow matching. They support five control types: beats, vocals, accompaniment, prosody, and reference audio. A shared variational autoencoder maps conditioning waveforms into a common latent space, enabling their attention memories to be combined. With the template timestep fixed at the clean-data endpoint and other inputs held constant, each control cache is computed once and reused throughout sampling. Training pairs are derived from music recordings using beat extraction, source separation, vocal resynthesis, and reference-excerpt selection. Single-control evaluations on Mandarin and English songs demonstrate improved adherence across all five control types and better lyric fidelity under vocal conditioning relative to the backbone. Automatic music-quality and instruction-following scores remain broadly comparable to those of the evaluated base models, with metric-specific trade-offs. We release the three template models to support research and creative applications in controllable music generation.

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: https://github.com/xingy038/Dreamer-XL.

Probability estimation models play an important role in various fields, such as weather forecasting, recommendation systems, and sports analysis. Among several models estimating probabilities, it is difficult to evaluate which model gives reliable probabilities since the ground-truth probabilities are not available. The win probability estimation model for esports, which calculates the win probability under a certain game state, is also one of the fields being actively studied in probability estimation. However, most of the previous works evaluated their models using accuracy, a metric that only can measure the performance of discrimination. In this work, we firstly investigate the Brier score and the Expected Calibration Error (ECE) as a replacement of accuracy used as a performance evaluation metric for win probability estimation models in esports field. Based on the analysis, we propose a novel metric called Balance score which is a simple yet effective metric in terms of six good properties that probability estimation metric should have. Under the general condition, we also found that the Balance score can be an effective approximation of the true expected calibration error which has been imperfectly approximated by ECE using the binning technique. Extensive evaluations using simulation studies and real game snapshot data demonstrate the promising potential to adopt the proposed metric not only for the win probability estimation model for esports but also for evaluating general probability estimation models.