  Since its foundations, more than one hundred years ago, the field of
structural biology has strived to understand and analyze the properties of
molecules and their interactions by studying the structure that they take in 3D
space. However, a fundamental challenge with this approach has been the dynamic
nature of these particles, which forces us to model not a single but a whole
distribution of structures for every molecular system. This thesis proposes
Intrinsic Diffusion Modeling, a novel approach to this problem based on
combining diffusion generative models with scientific knowledge about the
flexibility of biological complexes. The knowledge of these degrees of freedom
is translated into the definition of a manifold over which the diffusion
process is defined. This manifold significantly reduces the dimensionality and
increases the smoothness of the generation space allowing for significantly
faster and more accurate generative processes. We demonstrate the effectiveness
of this approach on two fundamental tasks at the basis of computational
chemistry and biology: molecular conformer generation and molecular docking. In
both tasks, we construct the first deep learning method to outperform
traditional computational approaches achieving an unprecedented level of
accuracy for scalable programs.
