This paper proposes DiffCSP++, a diffusion-based method for crystal generation that incorporates space group constraints. The method decomposes complex space group constraints into invariant lattice representations of different crystal families and symmetric atom types and coordinates according to Wyckoff positions, ensuring compatibility with the diffusion process. The key contributions include: (1) translating space group constraints into two tractable parts: the basis constraint of the O(3)-invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. (2) Generating lattices, fractional coordinates, and atom composition under the reduced form of the space group constraint through a novel denoising model that is E(3)-invariant. (3) Extensive experiments show that the method respects space group constraints and achieves promising performance in crystal structure prediction and ab initio crystal generation. The method is evaluated on several popular datasets, demonstrating its effectiveness in generating crystals with desired space group symmetries. The results show that DiffCSP++ outperforms existing methods in crystal structure prediction and ab initio generation tasks. The method enables the generation of diverse structures from the same composition but based on different space groups, opening up new opportunities for material design.This paper proposes DiffCSP++, a diffusion-based method for crystal generation that incorporates space group constraints. The method decomposes complex space group constraints into invariant lattice representations of different crystal families and symmetric atom types and coordinates according to Wyckoff positions, ensuring compatibility with the diffusion process. The key contributions include: (1) translating space group constraints into two tractable parts: the basis constraint of the O(3)-invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. (2) Generating lattices, fractional coordinates, and atom composition under the reduced form of the space group constraint through a novel denoising model that is E(3)-invariant. (3) Extensive experiments show that the method respects space group constraints and achieves promising performance in crystal structure prediction and ab initio crystal generation. The method is evaluated on several popular datasets, demonstrating its effectiveness in generating crystals with desired space group symmetries. The results show that DiffCSP++ outperforms existing methods in crystal structure prediction and ab initio generation tasks. The method enables the generation of diverse structures from the same composition but based on different space groups, opening up new opportunities for material design.