Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the target data distribution. As a result, the model must simultaneously represent the global structure of the distribution and its fine-scale local variations, which becomes difficult when these scales are strongly mismatched. This issue arises both in natural images, where coarse manifold-level structure and fine textures coexist, and in low-dimensional distributions with highly concentrated local structure. To address this issue, we propose Residual Prior Diffusion (RPD), a two-stage framework in which a coarse prior model first captures the large-scale structure of the data distribution, and a diffusion model is then trained to represent the residual between the prior and the target data distribution. We formulate RPD as an explicit probabilistic model with a tractable evidence lower bound, whose optimization reduces to the familiar objectives of noise prediction or velocity prediction. We further introduce auxiliary variables that leverage information from the prior model and theoretically analyze how they reduce the difficulty of the prediction problem in RPD. Experiments on synthetic datasets with fine-grained local structure show that standard diffusion models fail to capture local details, whereas RPD accurately captures fine-scale detail while preserving the large-scale structure of the distribution. On natural image generation tasks, RPD achieved generation quality that matched or exceeded that of representative diffusion-based baselines and it maintained strong performance even with a small number of inference steps.

Train-time data poisoning attacks threaten machine learning models by introducing adversarial examples during training, leading to misclassification. Current defense methods often reduce generalization performance, are attack-specific, and impose significant training overhead. To address this, we introduce a set of universal data purification methods using a stochastic transform, $\Psi(x)$, realized via iterative Langevin dynamics of Energy-Based Models (EBMs), Denoising Diffusion Probabilistic Models (DDPMs), or both. These approaches purify poisoned data with minimal impact on classifier generalization. Our specially trained EBMs and DDPMs provide state-of-the-art defense against various attacks (including Narcissus, Bullseye Polytope, Gradient Matching) on CIFAR-10, Tiny-ImageNet, and CINIC-10, without needing attack or classifier-specific information. We discuss performance trade-offs and show that our methods remain highly effective even with poisoned or distributionally shifted generative model training data.

The superior generation capabilities of Denoised Diffusion Probabilistic Models (DDPMs) have been effectively showcased across a multitude of domains. Recently, the application of DDPMs has extended to time series generation tasks, where they have significantly outperformed other deep generative models, often by a substantial margin. However, we have discovered two main challenges with these methods: 1) the inference time is excessively long; 2) there is potential for improvement in the quality of the generated time series. In this paper, we propose a method based on discrete token modeling technique called Similarity-driven Discrete Transformer (SDformer). Specifically, SDformer utilizes a similarity-driven vector quantization method for learning high-quality discrete token representations of time series, followed by a discrete Transformer for data distribution modeling at the token level. Comprehensive experiments show that our method significantly outperforms competing approaches in terms of the generated time series quality while also ensuring a short inference time. Furthermore, without requiring retraining, SDformer can be directly applied to predictive tasks and still achieve commendable results.

We provide the first polynomial-time convergence guarantees for the probabilistic flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (i.e., denoising diffusion probabilistic modeling or DDPM), but requires the development of novel techniques for studying deterministic dynamics without contractivity. Through the use of a specially chosen corrector step based on the underdamped Langevin diffusion, we obtain better dimension dependence than prior works on DDPM ($O(\sqrt d)$ vs. $O(d)$, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.

Speech enhancement (SE) aims to improve the intelligibility and quality of speech in the presence of non-stationary additive noise. Deterministic deep learning models have traditionally been used for SE, but recent studies have shown that generative approaches, such as denoising diffusion probabilistic models (DDPMs), can also be effective. However, incorporating condition information into DDPMs for SE remains a challenge. We propose a model-agnostic method called DOSE that employs two efficient condition-augmentation techniques to address this challenge, based on two key insights: (1) We force the model to prioritize the condition factor when generating samples by training it with dropout operation; (2) We inject the condition information into the sampling process by providing an informative adaptive prior. Experiments demonstrate that our approach yields substantial improvements in high-quality and stable speech generation, consistency with the condition factor, and inference efficiency.

Denoising Diffusion Probabilistic Models (DDPM) have recently gained significant attention. DDPMs compose a Markovian process that begins in the data domain and gradually adds noise until reaching pure white noise. DDPMs generate high-quality samples from complex data distributions by defining an inverse process and training a deep neural network to learn this mapping. However, these models are inefficient because they require many diffusion steps to produce aesthetically pleasing samples. Additionally, unlike generative adversarial networks (GANs), the latent space of diffusion models is less interpretable.

Diffusion models are capable of generating photo-realistic images that combine elements which do not appear together in natural images, demonstrating their ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Here, we consider a highly reduced setting to examine whether diffusion models learn semantically meaningful and fully factorized representations of composable features. We performed extensive controlled experiments on conditional DDPMs trained to generate various forms of 2D Gaussian data. We demonstrate that the models learn factorized, semi-continuous manifold representations that are orthogonal in underlying continuous latent features of independent variations but are not aligned for different values of the same feature. With such representations, models demonstrate superior compositionality but have limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with a small amount of compositional examples, suggesting a novel way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, thereby offering insights into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data, paving the way for future research aimed at enhancing factorization and compositional generalization in generative models for real-world applications.

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Diffusion models have achieved remarkable success in image synthesis. However, addressing artifacts and unrealistic regions remains a critical challenge. We propose self-refining diffusion, a novel framework that enhances image generation quality by detecting these flaws. The framework employs an explainable artificial intelligence (XAI)-based flaw highlighter to produce flaw activation maps (FAMs) that identify artifacts and unrealistic regions. These FAMs improve reconstruction quality by amplifying noise in flawed regions during the forward process and by focusing on these regions during the reverse process. The proposed approach achieves up to a 27.3% improvement in Fréchet inception distance across various diffusion-based models, demonstrating consistently strong performance on diverse datasets. It also shows robust effectiveness across different tasks, including image generation, text-to-image generation, and inpainting. These results demonstrate that explainable AI techniques can extend beyond interpretability to actively contribute to image refinement. The proposed framework offers a versatile and effective approach applicable to various diffusion models and tasks, significantly advancing the field of image synthesis.

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.