Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives -- as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to the addition of noise than baseline parameter inference networks.

翻译：扩散生成模型在跨领域的多样图像生成与重建任务中表现卓越，但其在涉及回归或分类问题的判别任务中的应用尚未得到充分探索。现代宇宙学的基石在于能够根据理论预测观测天体物理场的生成结果，并利用这些预测通过观测数据约束物理模型。本研究采用单一扩散生成模型实现上述相互关联的目标——既作为条件于输入宇宙学参数的冷暗物质密度场的代理模型或模拟器，又作为解决逆向问题（约束输入场的宇宙学参数）的参数推断模型。该模型能够生成与模拟目标分布具有一致汇总统计量的场。进而，我们利用扩散生成模型的近似似然函数，通过汉密尔顿蒙特卡洛方法对给定测试图像的宇宙学参数后验进行采样，从而推导出对宇宙学参数的严格约束。最后，我们证明相较于基线参数推断网络，该参数推断方法对噪声的加入具有更强的鲁棒性。