  Many protein design applications, such as binder or enzyme design, require
scaffolding a structural motif with high precision. Generative modelling
paradigms based on denoising diffusion processes emerged as a leading candidate
to address this motif scaffolding problem and have shown early experimental
success in some cases. In the diffusion paradigm, motif scaffolding is treated
as a conditional generation task, and several conditional generation protocols
were proposed or imported from the Computer Vision literature. However, most of
these protocols are motivated heuristically, e.g. via analogies to Langevin
dynamics, and lack a unifying framework, obscuring connections between the
different approaches. In this work, we unify conditional training and
conditional sampling procedures under one common framework based on the
mathematically well-understood Doob's h-transform. This new perspective allows
us to draw connections between existing methods and propose a new variation on
existing conditional training protocols. We illustrate the effectiveness of
this new protocol in both, image outpainting and motif scaffolding and find
that it outperforms standard methods.
