Generalization of Diffusion Models Arises with a Balanced Representation Space

Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective. We analyze the distinctions between memorization and generalization in diffusion models through the lens of representation learning. By investigating a two-layer ReLU denoising autoencoder (DAE), we prove that (i) memorization corresponds to the model storing raw training samples in the learned weights for encoding and decoding, yielding localized "spiky" representations, whereas (ii) generalization arises when the model captures local data statistics, producing "balanced" representations. Furthermore, we validate these theoretical findings on real-world unconditional and text-to-image diffusion models, demonstrating that the same representation structures emerge in deep generative models with significant practical implications. Building on these insights, we propose a representation-based method for detecting memorization and a training-free editing technique that allows precise control via representation steering. Together, our results highlight that learning good representations is central to novel and meaningful generative modeling.

Coarse-to-Fine Hierarchical Alignment for UAV-based Human Detection using Diffusion Models

Training object detectors demands extensive, task-specific annotations, yet this requirement becomes impractical in UAV-based human detection due to constantly shifting target distributions and the scarcity of labeled images. As a remedy, synthetic simulators are adopted to generate annotated data, with a low annotation cost. However, the domain gap between synthetic and real images hinders the model from being effectively applied to the target domain. Accordingly, we introduce Coarse-to-Fine Hierarchical Alignment (CFHA), a three-stage diffusion-based framework designed to transform synthetic data for UAV-based human detection, narrowing the domain gap while preserving the original synthetic labels. CFHA explicitly decouples global style and local content domain discrepancies and bridges those gaps using three modules: (1) Global Style Transfer -- a diffusion model aligns color, illumination, and texture statistics of synthetic images to the realistic style, using only a small real reference set; (2) Local Refinement -- a super-resolution diffusion model is used to facilitate fine-grained and photorealistic details for the small objects, such as human instances, preserving shape and boundary integrity; (3) Hallucination Removal -- a module that filters out human instances whose visual attributes do not align with real-world data to make the human appearance closer to the target distribution. Extensive experiments on public UAV Sim2Real detection benchmarks demonstrate that our methods significantly improve the detection accuracy compared to the non-transformed baselines. Specifically, our method achieves up to $+14.1$ improvement of mAP50 on Semantic-Drone benchmark. Ablation studies confirm the complementary roles of the global and local stages and highlight the importance of hierarchical alignment. The code is released at \href{https://github.com/liwd190019/CFHA}{this url}.

NERD: Network-Regularized Diffusion Sampling For 3D Computed Tomography

Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces measurement consistency, forward diffusion consistency, and both step-wise and backward diffusion consistency. However, these methods have only considered 2D reconstruction tasks and do not directly extend to 3D image reconstruction problems, such as in Computed Tomography (CT). To bridge this gap, we propose NEtwork-Regularized diffusion sampling for 3D CT (NERD) by incorporating an L1 regularization into the optimization objective. This regularizer encourages spatial continuity across adjacent slices, reducing inter-slice artifacts and promoting coherent volumetric reconstructions. Additionally, we introduce two efficient optimization strategies to solve the resulting objective: one based on the Alternating Direction Method of Multipliers (ADMM) and another based on the Primal-Dual Hybrid Gradient (PDHG) method. Experiments on medical 3D CT data demonstrate that our approach achieves either state-of-the-art or highly competitive results.

AlphaFlow: Understanding and Improving MeanFlow Models

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce $\alpha$-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, $\alpha$-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, $\alpha$-Flow consistently outperforms MeanFlow across scales and settings. Our largest $\alpha$-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

Attention-Only Transformers via Unrolled Subspace Denoising

Despite the popularity of transformers in practice, their architectures are empirically designed and neither mathematically justified nor interpretable. Moreover, as indicated by many empirical studies, some components of transformer architectures may be redundant. To derive a fully interpretable transformer architecture with only necessary components, we contend that the goal of representation learning is to compress a set of noisy initial token representations towards a mixture of low-dimensional subspaces. To compress these noisy token representations, an associated denoising operation naturally takes the form of a multi-head (subspace) self-attention. By unrolling such iterative denoising operations into a deep network, we arrive at a highly compact architecture that consists of \textit{only} self-attention operators with skip connections at each layer. Moreover, we show that each layer performs highly efficient denoising: it improves the signal-to-noise ratio of token representations \textit{at a linear rate} with respect to the number of layers. Despite its simplicity, extensive experiments on vision and language tasks demonstrate that such a transformer achieves performance close to that of standard transformer architectures such as GPT-2 and CRATE.

Understanding Generalization in Diffusion Models via Probability Flow Distance

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality samples that generalize beyond the training data. However, evaluating this generalization remains challenging: theoretical metrics are often impractical for high-dimensional data, while no practical metrics rigorously measure generalization. In this work, we bridge this gap by introducing probability flow distance ($\texttt{PFD}$), a theoretically grounded and computationally efficient metric to measure distributional generalization. Specifically, $\texttt{PFD}$ quantifies the distance between distributions by comparing their noise-to-data mappings induced by the probability flow ODE. Moreover, by using $\texttt{PFD}$ under a teacher-student evaluation protocol, we empirically uncover several key generalization behaviors in diffusion models, including: (1) scaling behavior from memorization to generalization, (2) early learning and double descent training dynamics, and (3) bias-variance decomposition. Beyond these insights, our work lays a foundation for future empirical and theoretical studies on generalization in diffusion models.

Towards Understanding the Mechanisms of Classifier-Free Guidance

Classifier-free guidance (CFG) is a core technique powering state-of-the-art image generation systems, yet its underlying mechanisms remain poorly understood. In this work, we begin by analyzing CFG in a simplified linear diffusion model, where we show its behavior closely resembles that observed in the nonlinear case. Our analysis reveals that linear CFG improves generation quality via three distinct components: (i) a mean-shift term that approximately steers samples in the direction of class means, (ii) a positive Contrastive Principal Components (CPC) term that amplifies class-specific features, and (iii) a negative CPC term that suppresses generic features prevalent in unconditional data. We then verify that these insights in real-world, nonlinear diffusion models: over a broad range of noise levels, linear CFG resembles the behavior of its nonlinear counterpart. Although the two eventually diverge at low noise levels, we discuss how the insights from the linear analysis still shed light on the CFG's mechanism in the nonlinear regime.

Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective

This work aims to demystify the out-of-distribution (OOD) capabilities of in-context learning (ICL) by studying linear regression tasks parameterized with low-rank covariance matrices. With such a parameterization, we can model distribution shifts as a varying angle between the subspace of the training and testing covariance matrices. We prove that a single-layer linear attention model incurs a test risk with a non-negligible dependence on the angle, illustrating that ICL is not robust to such distribution shifts. However, using this framework, we also prove an interesting property of ICL: when trained on task vectors drawn from a union of low-dimensional subspaces, ICL can generalize to any subspace within their span, given sufficiently long prompt lengths. This suggests that the OOD generalization ability of Transformers may actually stem from the new task lying within the span of those encountered during training. We empirically show that our results also hold for models such as GPT-2, and conclude with (i) experiments on how our observations extend to nonlinear function classes and (ii) results on how LoRA has the ability to capture distribution shifts.

UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weights

Recent advances in data-centric deep generative models have led to significant progress in solving inverse imaging problems. However, these models (e.g., diffusion models (DMs)) typically require large amounts of fully sampled (clean) training data, which is often impractical in medical and scientific settings such as dynamic imaging. On the other hand, training-data-free approaches like the Deep Image Prior (DIP) do not require clean ground-truth images but suffer from noise overfitting and can be computationally expensive as the network parameters need to be optimized for each measurement set independently. Moreover, DIP-based methods often overlook the potential of learning a prior using a small number of sub-sampled measurements (or degraded images) available during training. In this paper, we propose UGoDIT, an Unsupervised Group DIP via Transferable weights, designed for the low-data regime where only a very small number, M, of sub-sampled measurement vectors are available during training. Our method learns a set of transferable weights by optimizing a shared encoder and M disentangled decoders. At test time, we reconstruct the unseen degraded image using a DIP network, where part of the parameters are fixed to the learned weights, while the remaining are optimized to enforce measurement consistency. We evaluate UGoDIT on both medical (multi-coil MRI) and natural (super resolution and non-linear deblurring) image recovery tasks under various settings. Compared to recent standalone DIP methods, UGoDIT provides accelerated convergence and notable improvement in reconstruction quality. Furthermore, our method achieves performance competitive with SOTA DM-based and supervised approaches, despite not requiring large amounts of clean training data.

The Dual Power of Interpretable Token Embeddings: Jailbreaking Attacks and Defenses for Diffusion Model Unlearning

Despite the remarkable generalization capabilities of diffusion models, recent studies have shown that these models can memorize and generate harmful content when prompted with specific text instructions. Although fine-tuning approaches have been developed to mitigate this issue by unlearning harmful concepts, these methods can be easily circumvented through jailbreaking attacks. This indicates that the harmful concept has not been fully erased from the model. However, existing attack methods, while effective, lack interpretability regarding why unlearned models still retain the concept, thereby hindering the development of defense strategies. In this work, we address these limitations by proposing an attack method that learns an orthogonal set of interpretable attack token embeddings. The attack token embeddings can be decomposed into human-interpretable textual elements, revealing that unlearned models still retain the target concept through implicit textual components. Furthermore, these attack token embeddings are robust and transferable across text prompts, initial noises, and unlearned models. Finally, leveraging this diverse set of embeddings, we design a defense method applicable to both our proposed attack and existing attack methods. Experimental results demonstrate the effectiveness of both our attack and defense strategies.