Nguyen Bt

Luca Ambrogioni, Giulio Franzese, Alberto Foresti et al.

How should a diffusion model decide which noise levels to train on, and how much? Despite the importance of this choice, current noise schedules are based largely on heuristics or empirical tuning. Here, we develop a general statistical framework for studying asymptotically optimal noise-level allocation in diffusion training. Our first main result concerns the fully coupled regime, where information can spread between different time points. Under convexity or Polyak-Lojasiewicz-type assumptions, we show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels. Our second main result specializes this framework to an idealized independent-learner regime, intended to model temporal specialization in neural networks. Under an additional feature-noise decoupling condition, a random-matrix analysis leads to an information-theoretic proxy: the decoupled sampling density is proportional to the square root of the generative entropy rate, the rate at which conditional entropy grows along the forward process. We test these predictions in controlled settings where the coupled objective can be optimized directly, including Dirac mixtures, low-dimensional manifolds, and MNIST. In these settings, the optimized schedules are consistently finite-support, while the smooth entropic proxy closely tracks the atomic optimum in neural-network models and breaks down mainly in the fully coupled parametric case, as the theory suggests. We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable. The results indicate that square-root entropy scheduling can substantially improve training efficiency on discrete domains and remains competitive with standard EDM-style heuristics on continuous images.

Duy M. H. Nguyen, Duy M. Nguyen, Huong Vu et al.

Until now, Coronavirus SARS-CoV-2 has caused more than 850,000 deaths and infected more than 27 million individuals in over 120 countries. Besides principal polymerase chain reaction (PCR) tests, automatically identifying positive samples based on computed tomography (CT) scans can present a promising option in the early diagnosis of COVID-19. Recently, there have been increasing efforts to utilize deep networks for COVID-19 diagnosis based on CT scans. While these approaches mostly focus on introducing novel architectures, transfer learning techniques, or construction large scale data, we propose a novel strategy to improve the performance of several baselines by leveraging multiple useful information sources relevant to doctors' judgments. Specifically, infected regions and heat maps extracted from learned networks are integrated with the global image via an attention mechanism during the learning process. This procedure not only makes our system more robust to noise but also guides the network focusing on local lesion areas. Extensive experiments illustrate the superior performance of our approach compared to recent baselines. Furthermore, our learned network guidance presents an explainable feature to doctors as we can understand the connection between input and output in a grey-box model.