Official Review · ICLR 2026

The paper proposed a probabilistic version of DiffusionNet learning the map from the irregular geometries and boundary conditions to the PDE solution. The key idea is to replace the deterministic diffusion operator in DiffusionNet by a stochastic diffusion operator, which is equivalent to placing a prior over the message passing step. Then the paper uses variational inference to estimate the predictive distribution of the solution field. 1. The paper is written clearly. 2. The method looks sound. 1. The motivation is a bit skeptical. There can be many simpler choices for learning a probabilistic version of DiffusionNet to enable UQ. The paper proposes a rather complex framework --- injecting noises via SDE in message passing, and performing amortized VI --- which does not seem a strong necessity. For instance, why not use MC dropout, Deep Ensemble, Laplace method, or SWA-Gaussian (SWAG)? These methods all require minor or even no modification of the existing model/training, with a little bit extra work. From the methodology perspective, it is unclear where the advantage of the proposed method stands out, in addition to extra complexity. 2. Empirical performance is not supportive. The experimental results do not demonstrate the proposed method can largely improve simpler alternatives. Looking at Table 2, the performance of DN-DO/LA/ME is often comparable to or even better than PDN. It strengthens the doubt about the meaning/necessity of PDN --- why not we retreat to these classical, simple yet also powerful probabilistic training method? Why should we develop a new method? 3. The experiments are not sufficient. Only two datasets are employed for testing, which is below the bar in this community. In addition, there is no standard deviations and significance analysis, making it hard to conclude whether or not there is a difference between PDN and competing methods. see above