We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an approximate inverse physics simulator and a learned correction function. A central insight of our work is that training the learned correction with a single-step loss is equivalent to a score matching objective, while recursively predicting longer parts of the trajectory during training relates to maximum likelihood training of a corresponding probability flow. We highlight the advantages of our algorithm compared to standard denoising score matching and implicit score matching, as well as fully learned baselines for a wide range of inverse physics problems. The resulting inverse solver has excellent accuracy and temporal stability and, in contrast to other learned inverse solvers, allows for sampling the posterior of the solutions.

翻译：我们提出通过利用扩散模型的最新进展来求解涉及物理系统时间演化的逆问题。我们的方法结合近似逆物理模拟器和学习校正函数，逐步将系统的当前状态向后回溯至时间步。本工作的核心洞见在于：使用单步损失训练学习校正函数等价于分数匹配目标，而在训练过程中递归预测轨迹中较长部分则对应于相应概率流的最大似然训练。我们重点阐述了该算法相较于标准去噪分数匹配、隐式分数匹配以及全学习基线方法在广泛逆物理问题中的优势。所提出的逆求解器具有优异的精度和时间稳定性，且与其他学习型逆求解器相比，能够对解的后验分布进行采样。