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With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…
Diffusion models exhibit impressive generative capabilities but are significantly impacted by exposure bias. In this paper, we make a key observation: the energy of predicted noisy samples in the reverse process continuously declines…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Diffusion models are typically trained using pointwise reconstruction objectives that are agnostic to the spectral and multi-scale structure of natural signals. We propose a loss-level spectral regularization framework that augments…
Wall-pressure fluctuations in turbulent boundary layers drive flow-induced noise, structural vibration, and hydroacoustic disturbances, especially in underwater and aerospace systems. Accurate prediction of their wavenumber-frequency…
We investigate the statistical accuracy of temporally interpolated spatiotemporal flow sequences between sparse, decorrelated snapshots of turbulent flow fields using conditional Denoising Diffusion Probabilistic Models (DDPMs). The…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the…
Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later…
Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…
Diffusion Probabilistic Models have demonstrated remarkable performance across a wide range of generative tasks. However, we have observed that these models often suffer from a Signal-to-Noise Ratio-timestep (SNR-t) bias. This bias refers…
Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based…
Standard diffusion models (DMs) rely on the total destruction of data into non-informative white noise, forcing the backward process to denoise from a fully unstructured noise state. While ensuring diversity, this results in a cumbersome…
We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber…
Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
Diffusion-based Deep Generative Models (DDGMs) offer state-of-the-art performance in generative modeling. Their main strength comes from their unique setup in which a model (the backward diffusion process) is trained to reverse the forward…
Analysis of galaxy--galaxy strong lensing systems is strongly dependent on any prior assumptions made about the appearance of the source. Here we present a method of imposing a data-driven prior / regularisation for source galaxies based on…
Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses…