Crystals are fundamental to numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods often overlook the crucial role of space group constraints, which are essential for describing the geometry of crystals and are closely related to many desirable properties. This paper addresses this gap by reducing the space group constraint into an equivalent formulation that is more tractable for integration into the generation process. Specifically, the space group constraint is translated into two parts: the basis constraint of the invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. Based on these derived constraints, the authors propose DiffCSP++, an enhanced version of the previous DiffCSP method, which incorporates space group constraints into the diffusion process. Experiments on several popular datasets demonstrate the effectiveness of the proposed method, showing promising performance in crystal structure prediction, ab initio crystal generation, and controllable generation with customized space groups.Crystals are fundamental to numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods often overlook the crucial role of space group constraints, which are essential for describing the geometry of crystals and are closely related to many desirable properties. This paper addresses this gap by reducing the space group constraint into an equivalent formulation that is more tractable for integration into the generation process. Specifically, the space group constraint is translated into two parts: the basis constraint of the invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. Based on these derived constraints, the authors propose DiffCSP++, an enhanced version of the previous DiffCSP method, which incorporates space group constraints into the diffusion process. Experiments on several popular datasets demonstrate the effectiveness of the proposed method, showing promising performance in crystal structure prediction, ab initio crystal generation, and controllable generation with customized space groups.