Peptide engineering has emerged as a critical discipline within biomedicine, finding applications in therapeutics, diagnostics, and synthetic biology. Despite their prevalence in biological processes, pursuing de novo therapeutic peptide design remains a formidable challenge. We here focus on generating helical peptides and present HelixDiff, a score-based diffusion model to learn and generate all-atom helical structures. We incorporate a hotspot-specific inpainting mechanism for the conditional design of α-helix structures that align with critical residues at protein-peptide interfaces. The results of our model showcase the production of helix structures with near-native geometries for a substantial portion of the test scenarios, showing root mean square deviations (RMSDs) less than 1Å. HelixDiff has shown better sequence recovery and Rosetta scores for unconditional and conditional generations than HelixGAN, our previous gan-based model. The case study involving glucagon-like peptide-1 (GLP-1) underscored HelixDiff's exceptional capacity to generate therapeutic D-peptides. The HelixDiff D-GLP-1 design is more stable than our earlier HelixGAN design when both D-peptides are bound to the GLP-1 receptor according to molecular dynamics simulations. The source code and data sets are available at github (https://github.com/xxiexuezhi/HelixDiff).