As our planet is entering into the "global boiling" era, understanding regional climate change becomes imperative. Effective downscaling methods that provide localized insights are crucial for this target. Traditional approaches, including computationally-demanding regional dynamical models or statistical downscaling frameworks, are often susceptible to the influence of downscaling uncertainty. Here, we address these limitations by introducing a diffusion probabilistic downscaling model (DPDM) into the meteorological field. This model can efficiently transform data from 1{\deg} to 0.1{\deg} resolution. Compared with deterministic downscaling schemes, it not only has more accurate local details, but also can generate a large number of ensemble members based on probability distribution sampling to evaluate the uncertainty of downscaling. Additionally, we apply the model to generate a 180-year dataset of monthly surface variables in East Asia, offering a more detailed perspective for understanding local scale climate change over the past centuries.

While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained with differential privacy (DP) on sensitive data can sidestep this challenge, providing access to synthetic data instead. We build on the recent success of diffusion models (DMs) and introduce Differentially Private Diffusion Models (DPDMs), which enforce privacy using differentially private stochastic gradient descent (DP-SGD). We investigate the DM parameterization and the sampling algorithm, which turn out to be crucial ingredients in DPDMs, and propose noise multiplicity, a powerful modification of DP-SGD tailored to the training of DMs. We validate our novel DPDMs on image generation benchmarks and achieve state-of-the-art performance in all experiments. Moreover, on standard benchmarks, classifiers trained on DPDM-generated synthetic data perform on par with task-specific DP-SGD-trained classifiers, which has not been demonstrated before for DP generative models.