NnD: Diffusion-based Generation of Physically-Nonnegative Objects

Most natural objects have inherent complexity and variability. While some simple objects can be modeled from first principles, many real-world phenomena, such as cloud formation, require computationally expensive simulations that limit scalability. This work focuses on a class of physically meaningful, nonnegative objects that are computationally tractable but costly to simulate. To dramatically reduce computational costs, we propose nonnegative diffusion (NnD). This is a learned generative model using score based diffusion. It adapts annealed Langevin dynamics to enforce, by design, non-negativity throughout iterative scene generation and analysis (inference). NnD trains on high-quality physically simulated objects. Once trained, it can be used for generation and inference. We demonstrate generation of 3D volumetric clouds, comprising inherently nonnegative microphysical fields. Our generated clouds are consistent with cloud physics trends. They are effectively not distinguished as non-physical by expert perception.

Towards A Most Probable Recovery in Optical Imaging

Light is a complex-valued field. The intensity and phase of the field are affected by imaged objects. However, imaging sensors measure only real-valued non-negative intensities. This results in a nonlinear relation between the measurements and the unknown imaged objects. Moreover, the sensor readouts are corrupted by Poissonian-distributed photon noise. In this work, we seek the most probable object (or clear image), given noisy measurements, that is, maximizing the a-posteriori probability of the sought variables. Hence, we generalize annealed Langevin dynamics, tackling fundamental challenges in optical imaging, including phase recovery and Poisson (photon) denoising. We leverage deep neural networks, not for explicit recovery of the imaged object, but as an approximate gradient for a prior term. We show results on empirical data, acquired by a real experiment. We further show results of simulations.