Visibility-Guided Structured Measure Flow for Class-Conditioned 3D Gaussian Generation

3D Gaussian Splatting (3DGS) has made real-time, high-fidelity 3D rendering practical, yet turning this explicit representation into a native generative space remains an open challenge. Directly generating 3DGS objects is difficult because Gaussian primitives are unordered, variable-sized, locally dense, and highly sensitive to rendering behavior. We present VISTA-GS, a visibility-guided structured measure flow framework for class-conditioned 3D Gaussian generation. Instead of treating a 3DGS object as a flat primitive sequence or a generic latent token grid, we formulate it as a structured Gaussian measure weighted by opacity, anisotropic covariance, and multi-view visibility. Based on this formulation, we introduce a visibility-aware measure VAE that learns permutation-invariant, variable-size-compatible, and rendering-aware latent representations of 3DGS objects. We further develop a renderer-consistent measure flow that transports class-conditioned priors toward the learned 3DGS measure distribution while aligning the decoded objects with their multi-view rendering distributions. To preserve object layout and local details, VISTA-GS incorporates structure-preserving patch transport that couples global class semantics, local Gaussian measure patches, and spatial anchors during flow prediction. On VISTA-Obj30, VISTA-GS improves over the strongest baseline by roughly 60--72% across geometry, appearance, view-consistency error, and generation speed. This design enables efficient generation of coherent, detailed, and view-consistent 3D Gaussian objects without relying on per-instance optimization, multi-view image synthesis, or reconstruction-based lifting pipelines. Project code and model checkpoints will be released.