Transforming 2D MNIST into rich 3D geometries (watertight meshes, sparse SDFs, and 6D normal-oriented point clouds) with continuous flow matching generative pipelines.
Continuous 3D mesh synthesis conditioned directly on sparse input point clouds ($N = 512$ with oriented normals). Stage 1 (Point-Conditioned Structure DiT MeanFlow) predicts active voxel occupancy grids, followed by Stage 2 (Sparse Vertex SDF Rectified Flow) predicting continuous 1D Signed Distance Fields decoded into watertight triangle meshes via Differentiable Marching Cubes.
Two-Stage Geometric Pipeline: Input Point Cloud ($N=512$, $6\text{D}$) $\to$ Stage 1 Predicted Sparse Voxels $\to$ Stage 2 Watertight Triangle Mesh via Differentiable Marching Cubes.