Gradient-based optimization with categorical variables typically relies on score-function estimators, which are unbiased but noisy, or on continuous relaxations that replace the discrete distribution with a smooth surrogate admitting a pathwise (reparameterized) gradient, at the cost of optimizing a biased, temperature-dependent objective. In this paper, we extend this family of relaxations by introducing a diffusion-based soft reparameterization for categorical distributions. For these distributions, the denoiser under a Gaussian noising process admits a closed form and can be computed efficiently, yielding a training-free diffusion sampler through which we can backpropagate. Our experiments show that the proposed reparameterization trick yields competitive or improved optimization performance on various benchmarks.

Aligning diffusion models to downstream tasks often requires finetuning new models or gradient-based guidance at inference time to enable sampling from the reward-tilted posterior. In this work, we explore a simple inference-time gradient-free guidance approach, called controlled denoising (CoDe), that circumvents the need for differentiable guidance functions and model finetuning. CoDe is a blockwise sampling method applied during intermediate denoising steps, allowing for alignment with downstream rewards. Our experiments demonstrate that, despite its simplicity, CoDe offers a favorable trade-off between reward alignment, prompt instruction following, and inference cost, achieving a competitive performance against the state-of-the-art baselines. Our code is available at: https://github.com/anujinho/code.

Cross-view geo-localization in GNSS-denied environments aims to determine an unknown location by matching drone-view images with the correct geo-tagged satellite-view images from a large gallery. Recent research shows that learning discriminative image representations under specific weather conditions can significantly enhance performance. However, the frequent occurrence of unseen extreme weather conditions hinders progress. This paper introduces MCGF, a Multi-weather Cross-view Geo-localization Framework designed to dynamically adapt to unseen weather conditions. MCGF establishes a joint optimization between image restoration and geo-localization using denoising diffusion models. For image restoration, MCGF incorporates a shared encoder and a lightweight restoration module to help the backbone eliminate weather-specific information. For geo-localization, MCGF uses EVA-02 as a backbone for feature extraction, with cross-entropy loss for training and cosine distance for testing. Extensive experiments on University160k-WX demonstrate that MCGF achieves competitive results for geo-localization in varying weather conditions.

In this study, we examine the representation learning abilities of Denoising Diffusion Models (DDM) that were originally purposed for image generation. Our philosophy is to deconstruct a DDM, gradually transforming it into a classical Denoising Autoencoder (DAE). This deconstructive procedure allows us to explore how various components of modern DDMs influence self-supervised representation learning. We observe that only a very few modern components are critical for learning good representations, while many others are nonessential. Our study ultimately arrives at an approach that is highly simplified and to a large extent resembles a classical DAE. We hope our study will rekindle interest in a family of classical methods within the realm of modern self-supervised learning.

Anomaly detection in multivariate time series has emerged as a crucial challenge in time series research, with significant research implications in various fields such as fraud detection, fault diagnosis, and system state estimation. Reconstruction-based models have shown promising potential in recent years for detecting anomalies in time series data. However, due to the rapid increase in data scale and dimensionality, the issues of noise and Weak Identity Mapping (WIM) during time series reconstruction have become increasingly pronounced. To address this, we introduce a novel Adaptive Dynamic Neighbor Mask (ADNM) mechanism and integrate it with the Transformer and Denoising Diffusion Model, creating a new framework for multivariate time series anomaly detection, named Denoising Diffusion Mask Transformer (DDMT). The ADNM module is introduced to mitigate information leakage between input and output features during data reconstruction, thereby alleviating the problem of WIM during reconstruction. The Denoising Diffusion Transformer (DDT) employs the Transformer as an internal neural network structure for Denoising Diffusion Model. It learns the stepwise generation process of time series data to model the probability distribution of the data, capturing normal data patterns and progressively restoring time series data by removing noise, resulting in a clear recovery of anomalies. To the best of our knowledge, this is the first model that combines Denoising Diffusion Model and the Transformer for multivariate time series anomaly detection. Experimental evaluations were conducted on five publicly available multivariate time series anomaly detection datasets. The results demonstrate that the model effectively identifies anomalies in time series data, achieving state-of-the-art performance in anomaly detection.

This paper introduces two key contributions aimed at improving the speed and quality of images generated through inverse diffusion processes. The first contribution involves reparameterizing the diffusion process in terms of the angle on a quarter-circular arc between the image and noise, specifically setting the conventional $\displaystyle \sqrt{\bar{\alpha}}=\cos(\eta)$. This reparameterization eliminates two singularities and allows for the expression of diffusion evolution as a well-behaved ordinary differential equation (ODE). In turn, this allows higher order ODE solvers such as Runge-Kutta methods to be used effectively. The second contribution is to directly estimate both the image ($\mathbf{x}_0$) and noise ($\mathbf{\epsilon}$) using our network, which enables more stable calculations of the update step in the inverse diffusion steps, as accurate estimation of both the image and noise are crucial at different stages of the process. Together with these changes, our model achieves faster generation, with the ability to converge on high-quality images more quickly, and higher quality of the generated images, as measured by metrics such as Frechet Inception Distance (FID), spatial Frechet Inception Distance (sFID), precision, and recall.

This dissertation attempts to drive innovation in the field of generative modeling for computer vision, by exploring novel formulations of conditional generative models, and innovative applications in images, 3D animations, and video. Our research focuses on architectures that offer reversible transformations of noise and visual data, and the application of encoder-decoder architectures for generative tasks and 3D content manipulation. In all instances, we incorporate conditional information to enhance the synthesis of visual data, improving the efficiency of the generation process as well as the generated content. We introduce the use of Neural ODEs to model video dynamics using an encoder-decoder architecture, demonstrating their ability to predict future video frames despite being trained solely to reconstruct current frames. Next, we propose a conditional variant of continuous normalizing flows that enables higher-resolution image generation based on lower-resolution input, achieving comparable image quality while reducing parameters and training time. Our next contribution presents a pipeline that takes human images as input, automatically aligns a user-specified 3D character with the pose of the human, and facilitates pose editing based on partial inputs. Next, we derive the relevant mathematical details for denoising diffusion models that use non-isotropic Gaussian processes, and show comparable generation quality. Finally, we devise a novel denoising diffusion framework capable of solving all three video tasks of prediction, generation, and interpolation. We perform ablation studies, and show SOTA results on multiple datasets. Our contributions are published articles at peer-reviewed venues. Overall, our research aims to make a meaningful contribution to the pursuit of more efficient and flexible generative models, with the potential to shape the future of computer vision.

In recent years, deep learning models have been successfully employed for augmenting low-resolution cosmological simulations with small-scale information, a task known as "super-resolution". So far, these cosmological super-resolution models have relied on generative adversarial networks (GANs), which can achieve highly realistic results, but suffer from various shortcomings (e.g. low sample diversity). We introduce denoising diffusion models as a powerful generative model for super-resolving cosmic large-scale structure predictions (as a first proof-of-concept in two dimensions). To obtain accurate results down to small scales, we develop a new "filter-boosted" training approach that redistributes the importance of different scales in the pixel-wise training objective. We demonstrate that our model not only produces convincing super-resolution images and power spectra consistent at the percent level, but is also able to reproduce the diversity of small-scale features consistent with a given low-resolution simulation. This enables uncertainty quantification for the generated small-scale features, which is critical for the usefulness of such super-resolution models as a viable surrogate model for cosmic structure formation.

We consider the image transmission problem over a noisy wireless channel via deep learning-based joint source-channel coding (DeepJSCC) along with a denoising diffusion probabilistic model (DDPM) at the receiver. Specifically, we are interested in the perception-distortion trade-off in the practical finite block length regime, in which separate source and channel coding can be highly suboptimal. We introduce a novel scheme that utilizes the range-null space decomposition of the target image. We transmit the range-space of the image after encoding and employ DDPM to progressively refine its null space contents. Through extensive experiments, we demonstrate significant improvements in distortion and perceptual quality of reconstructed images compared to standard DeepJSCC and the state-of-the-art generative learning-based method. We will publicly share our source code to facilitate further research and reproducibility.

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in other applications such as tabular and graph data generation. However, due to computational complexity, to this date, the application of these techniques to graph data has been restricted to small graphs, such as those used in molecular modeling. In this paper, we propose SaGess, a discrete denoising diffusion approach, which is able to generate large real-world networks by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. The algorithm is capable of generating larger graphs by sampling a covering of subgraphs of the initial graph in order to train DiGress. SaGess then constructs a synthetic graph using the subgraphs that have been generated by DiGress. We evaluate the quality of the synthetic data sets against several competitor methods by comparing graph statistics between the original and synthetic samples, as well as evaluating the utility of the synthetic data set produced by using it to train a task-driven model, namely link prediction. In our experiments, SaGess, outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor, both on the graph metrics and on the link prediction task.