This paper introduces PepGLAD, a generative model for full-atom peptide design using geometric latent diffusion. The model addresses two major challenges in peptide design: full-atom geometry and variable binding geometry. To tackle the first challenge, PepGLAD employs a variational autoencoder (VAE) to encode full-atom residues into fixed-dimensional latent representations, enabling efficient decoding. For the second challenge, a receptor-specific affine transformation is introduced to convert 3D coordinates into a shared standard space, enhancing generalization across different binding sites. The model is trained on a benchmark consisting of 1D sequences and 3D structures from the Protein Data Bank (PDB) and literature. Experimental results show that PepGLAD outperforms existing methods in terms of diversity, binding affinity, and success rate in sequence-structure co-design and binding conformation generation. The model also demonstrates strong performance in recovering reference structures for binding conformation generation. The key contributions include the construction of a new benchmark, the development of a VAE for full-atom geometry, and the introduction of a receptor-specific affine transformation for variable binding geometry. The model is designed to be $ E(3) $-equivariant, ensuring that the diffusion process is invariant to rigid transformations. The results demonstrate that PepGLAD achieves superior performance in generating peptides with high binding affinity and diverse conformations, making it a promising approach for peptide design.This paper introduces PepGLAD, a generative model for full-atom peptide design using geometric latent diffusion. The model addresses two major challenges in peptide design: full-atom geometry and variable binding geometry. To tackle the first challenge, PepGLAD employs a variational autoencoder (VAE) to encode full-atom residues into fixed-dimensional latent representations, enabling efficient decoding. For the second challenge, a receptor-specific affine transformation is introduced to convert 3D coordinates into a shared standard space, enhancing generalization across different binding sites. The model is trained on a benchmark consisting of 1D sequences and 3D structures from the Protein Data Bank (PDB) and literature. Experimental results show that PepGLAD outperforms existing methods in terms of diversity, binding affinity, and success rate in sequence-structure co-design and binding conformation generation. The model also demonstrates strong performance in recovering reference structures for binding conformation generation. The key contributions include the construction of a new benchmark, the development of a VAE for full-atom geometry, and the introduction of a receptor-specific affine transformation for variable binding geometry. The model is designed to be $ E(3) $-equivariant, ensuring that the diffusion process is invariant to rigid transformations. The results demonstrate that PepGLAD achieves superior performance in generating peptides with high binding affinity and diverse conformations, making it a promising approach for peptide design.