EMERGE: Resolution-Agnostic Point Cloud Generation with Equivariant Graph-Based Diffusion

Autoregressive models have emerged as an effective paradigm for point cloud generation. However, most existing approaches rely on heuristic tokenization strategies, such as spatial sorting or stochastic downsampling, which often disrupt intrinsic point cloud topology and weaken the structural coherence of the generated shapes. In this paper, we present PointRSP, an autoregressive framework that reformulates point cloud generation as a topology-preserving tessellation process via recursive spectral partitioning. Instead of constructing token sequences heuristically, we introduce a topology-aware partitioning autoencoder that decomposes an unstructured point cloud into a non-balanced binary tree through a hybrid recursive spectral partitioning strategy. This hierarchical representation provides a deterministic geometric blueprint that preserves topological relationships while capturing multiscale structural dependencies within a quantized latent space. To synthesize shapes in this space, we propose a dual-stream cascaded generator that jointly models structural evolution and feature synthesis. In addition, we design a geometry-calibrated positional encoding mechanism that anchors latent embeddings using multi-scale structural centers, which stabilizes cascaded generation during the early stages of structural formation. Extensive experiments show that PointRSP achieves state-of-the-art performance in generation quality and diversity, demonstrating strong generalization across complex 3D topologies.

Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a \textit{Latent Flow Matching} models the global shape manifold in a compact latent space, and a \textit{Conditional Point Flow Matching} reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.

Generating realistic 3D city environments from remote sensing data is important for simulation, urban planning, and mixed reality, yet existing point cloud generation methods are limited to single objects or bounded indoor scenes and cannot handle the scale, seamless tiling, and partial observability challenges of city-scale generation. We present \ours{}, a multi-stage framework that generates dense, colored point clouds ($10^5$ points per $150\text{m}{\times}150\text{m}$ tile) at city scale, conditioned on satellite imagery, semantic segmentation maps, and digital surface models (DSM). A \emph{Grid-Aligned VAE} encodes each tile into a topology-preserving latent grid where tokens correspond to fixed spatial regions, enabling spatially coherent multi-modal conditioning and compact latent-space edge consistency that implicitly aligns thousands of boundary points for seamless cross-tile generation. A conditional rectified flow model synthesizes geometry latents from the fused multi-modal conditions, and an orientation-aware diffusion colorizer separately handles satellite-visible horizontal surfaces and occluded vertical façades. To support standardized evaluation, we build on public 3D data sources to introduce \emph{City3D-MultiGen}, a benchmark of $163$K densely annotated tiles from Melbourne and London with aligned point clouds, satellite images, semantic maps, and elevation data. Experiments show that \ours{} outperforms adapted point cloud generation baselines across all geometry metrics and produces visually coherent colored point clouds with seamless boundaries over arbitrarily large urban extents. Our benchmark details are available at https://huggingface.co/datasets/e32/City3D-MultiGen