Generating physically stable 3D structures from visual specifications requires resolving geometric ambiguity while accounting for physical interactions among objects. We present StackGen3D, a framework for generating stable block assemblies conditioned on a given block inventory and three orthographic silhouettes. Our approach consists of two stages. First, we develop a physics-informed graph neural network (PI-GNN) that models support relations between blocks and serves as a fast stability predictor for curating a diverse dataset of stable structures. Second, we train a conditional flow-matching model on this dataset to capture the multimodal distribution of block configurations consistent with the target silhouettes. At inference time, lightweight geometric selection and refinement reduce inter-block penetration without physics simulation. Preliminary experiments show that the PI-GNN generalizes from simple stacks to complex structures substantially better than a parameter-matched multilayer perceptron. For structure generation, Best-of-10 selection improves physical stability from 45.3% to 72.4% while achieving a silhouette IoU of 0.970. These results highlight the potential of combining relational physical reasoning, scalable data curation, and conditional generative modeling for creative 3D assembly. Project website: https://ripl.github.io/StackGen3D-web/
Figures & tables
Figure 1: PI-GNN Training Process.
Inference method
Stability (%)
IoU
Penetration
Single sample ( N=1 )
45.30±4.10
.967±.002
.711±.066
Best-of-5
66.70±4.61
.970±.002
.134±.026
Best-of-10
72.40±4.63
.970±.002
.064±.016
Best-of-25
67.80±5.15
.970±.002
.034±.005
Best-of-50
69.30±4.94
.969±.002
.028±.003
Best-of-100
66.00±4.05
.969±.003
.025±.002
Table 1: Best-of-N generation (mean ± std. over 10 folds).
Figure 2: Qualitative PI-GNN stability predictions on complex structures. Block-level predictions are compared with MuJoCo labels, illustrating how learned support reasoning transfers from simple structures to complex.
Figure 3: Qualitative conditional flow-matching generations. Each example shows the input orthographic silhouettes, reference structure, generated structure before simulation, and its configuration after post-hoc physics simulation.
Most existing 3D assembly methods treat the problem as pure pose estimation, rearranging observed parts via rigid transformations. In contrast, human assembly naturally couples structural reasoning with holistic shape inference. Inspired by this intuition, we reformulate 3D assembly as a joint problem of assembly and generation. We show that these two processes are mutually reinforcing: assembly provides part-level structural priors for generation, while generation injects holistic shape context that resolves ambiguities in assembly. Unlike prior methods that cannot synthesize missing geometry, we propose CRAG, which simultaneously generates plausible complete shapes and predicts poses for input parts. Extensive experiments demonstrate state-of-the-art performance across in-the-wild objects with diverse geometries, varying part counts, and missing pieces. Project Page: https://ai4ce.github.io/CRAG/
Part-aware 3D asset generation enables applications such as editing, articulation, simulation, and fabrication, yet existing methods can generate visually complete individual parts without ensuring that they form a valid physical assembly. Consequently, generated neighboring parts may interpenetrate, lack valid connections, or collapse under gravity. We propose a physics-guided framework for improving single-image part-aware 3D generation with physically compatible geometry and stable connections. Our method resolves inter-part penetration, recovers a contact graph between neighboring parts, and introduces parameterized connectors at their contact surfaces. Using feedback from physical simulation, we refine connector placement, orientation, and dimensions to improve assembly stability while preserving the generated geometry. We further introduce a physics-based evaluation protocol that complements conventional geometric metrics by directly testing assembly validity and stability under gravity. Experiments comparing against multiple part-aware 3D generators show substantial improvements in physical realizability and stability while maintaining geometric quality. We additionally validate the resulting parts through 3D printing and real-world assembly.
While autoregressive models have advanced 3D generation, creating physically stable brick structures remains a challenge due to the strict requirements of gravity and interconnectivity. Existing approaches rely on external physical simulators during inference to perform rejection sampling and brick-by-brick rollbacks, which severely bottlenecks efficiency. To address this, we propose a reinforcement learning paradigm that shifts physical validity enforcement from test-time correction to training-time policy optimization. By utilizing assembly-level rewards, the model optimizes for collision avoidance, global connectivity, structural interlocking, and shape conformity. This paradigm allows the model to internalize physical priors, enabling the first rollback-free generation of stable brick structures. Experimental results demonstrate that our approach achieves state-of-the-art generation quality while accelerating inference speed by orders of magnitude. Our code and dataset are available at https://github.com/miniHuiHui/STABLE. Our models are available at https://huggingface.co/miniHui/STABLE.
Chenhui Xu, Ziyue Bai, Fuxun Yu +2
University of Buffalo · University of Maryland, College Park · Microsoft +1