Spectral graph generation models represent a graph by the eigenvalues and eigenvectors of its Laplacian, offering a compact continuous alternative to explicit edge construction. These eigensystems must respect three Laplacian constraints: orthonormal eigenvectors, non‑negative eigenvalues, and a nullspace spanned by the constant vector. Existing approaches enforce orthonormality but ignore the nullspace condition, which can produce eigensystems incompatible with any valid Laplacian. We introduce Laplacian‑Constrained Stiefel Flow Matching (LaSFM), which simultaneously preserves orthonormality, positivity of eigenvalues, and the nullspace during generation. We first characterize the constrained Stiefel manifold, derive the flow‑matching dynamics on it, and implement a neural ODE that evolves the system in continuous time. LaSFM also supports property‑guided generation: by adding a gradient term for desired graph attributes (e.g., degree distribution, clustering coefficient) while keeping the constraints, samples are steered toward target properties. Experiments on several benchmark datasets show that LaSFM improves both spectral metrics (eigenvalue distribution, eigenvector similarity) and graph‑level metrics (edge count, connectivity), and achieves better alignment with specified properties.\n\nReview