In this section we provide full descriptions of the diffusion processes introduced in Sec. 3 .

A popular approach to protein design is to combine a generative model with a discriminative model for conditional sampling.

With the emergence of various molecular tasks and massive datasets, how to perform efficient training has become an urgent yet under-explored issue in the area. Data pruning (DP), as an oft-stated approach to saving training burdens, filters out less influential samples to form a coreset for training.

However,inmanyreal-worldtasks,the learned function is intended to satisfy domain-specific constraints. We focus on monotonicity constraints, which are common and require that the function's output increases with increasing values of specific input features.

Below, we proceed to describe our contributions in greater detail. Our framework builds upon the seminal work of Jordan et al. [1998], which introduced the celebrated