  Have you ever been troubled by the complexity and computational cost of SE(3)
protein structure modeling and been amazed by the simplicity and power of
language modeling? Recent work has shown promise in simplifying protein
structures as sequences of protein angles; therefore, language models could be
used for unconstrained protein backbone generation. Unfortunately, such
simplification is unsuitable for the constrained protein inpainting problem,
where the model needs to recover masked structures conditioned on unmasked
ones, as it dramatically increases the computing cost of geometric constraints.
To overcome this dilemma, we suggest inserting a hidden \textbf{a}tomic
\textbf{d}irection \textbf{s}pace (\textbf{ADS}) upon the language model,
converting invariant backbone angles into equivalent direction vectors and
preserving the simplicity, called Seq2Direct encoder ($\text{Enc}_{s2d}$).
Geometric constraints could be efficiently imposed on the newly introduced
direction space. A Direct2Seq decoder ($\text{Dec}_{d2s}$) with mathematical
guarantees is also introduced to develop a \textbf{SDS}
($\text{Enc}_{s2d}$+$\text{Dec}_{d2s}$) model. We apply the SDS model as the
denoising neural network during the conditional diffusion process, resulting in
a constrained generative model--\textbf{DiffSDS}. Extensive experiments show
that the plug-and-play ADS could transform the language model into a strong
structural model without loss of simplicity. More importantly, the proposed
DiffSDS outperforms previous strong baselines by a large margin on the task of
protein inpainting.
