Researchers have identified a problem with how generative models are applied to certain types of data, specifically those on Riemannian manifolds such as spheres and hyperbolic spaces. These models draw from a Gaussian distribution in the tangent space at a base point, but this can lead to a fixed distance distribution being used instead of the intended one. The researchers have developed a solution to this problem, deriving a closed-form expression for the tangent density that realizes the intended distance distribution. They also provide experiments demonstrating the effectiveness of their approach. --- Why it matters: This matters because generative models on Riemannian manifolds are widely used in applications such as protein structure prediction and image generation. The issue identified by the researchers can lead to biased results, particularly when dealing with data that has a complex geometric structure. By addressing this problem, the researchers' solution can improve the accuracy and reliability of these models. Source: https://arxiv.org/abs/2511.14056