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Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…
Recent text-to-image diffusion models generate high-quality images but struggle to learn new, personalized styles, which limits the creation of unique style templates. In style-driven generation, users typically supply reference images…
Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research.…
Image generation using diffusion can be controlled in multiple ways. In this paper, we systematically analyze the equations of modern generative diffusion networks to propose a framework, called MDP, that explains the design space of…
We present a method to determine the shot noise in quantum systems from knowledge of their time evolution - the latter being obtained using numerical simulation techniques. While our ultimate goal is the study of interacting systems, the…
As PET imaging is accompanied by substantial radiation exposure and cancer risk, reducing radiation dose in PET scans is an important topic. Recently, diffusion models have emerged as the new state-of-the-art generative model to generate…
In this work, we address the limitations of denoising diffusion models (DDMs) in image restoration tasks, particularly the shape and color distortions that can compromise image quality. While DDMs have demonstrated a promising performance…
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…
Assistive drawing aims to facilitate the creative process by providing intelligent guidance to artists. Existing solutions often fail to effectively model intricate stroke details or adequately address the temporal aspects of drawing. We…
Recent text-to-image (T2I) diffusion models have achieved remarkable advancement, yet faithfully following complex textual descriptions remains challenging due to insufficient interactions between textual and visual features. Prior…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a…
Diffusion models have been successfully adapted to text generation tasks by mapping the discrete text into the continuous space. However, there exist nonnegligible gaps between training and inference, owing to the absence of the forward…
Diffusion models that can generate high-quality data from randomly sampled Gaussian noises have become the mainstream generative method in both academia and industry. Are randomly sampled Gaussian noises equally good for diffusion models?…
Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as…
Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions, among other systems. Therefore, it is essential to…
Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is…