Maximilian Plattner | Searcharxiv

arXiv2026

Meltdown: Circuits and Bifurcations in Point-Cloud-Conditioned 3D Diffusion Transformers

Sparse point clouds are a common input modality for 3D surface reconstruction, including in safety-critical settings such as surgical navigation and autonomous perception. Recent point-cloud-conditioned 3D diffusion transformers achieve state-of-the-art results in this regime by leveraging learned priors. We show that these models can fail catastrophically under realistic input variation, and present a mechanistic case study of why. We identify a failure mode we call Meltdown: tiny on-surface perturbations to a sparse input point cloud can fracture the reconstructed output into hundreds of disconnected pieces. Adversarial search recovers Meltdown in 89.9-100% of shapes across the two open-weight state-of-the-art architectures we study (WaLa, Make-a-Shape) on real-world datasets (GSO, SimJEB) and under both DDPM and DDIM sampling. We trace Meltdown along the forward pass: it is governed by how uniformly the points are distributed on the surface, faithfully transduced through the point-cloud encoder, and committed by a single early-denoising cross-attention write in the diffusion backbone. Diffusion-trajectory ensembles exhibit symmetry-breaking near this commit step, consistent with a bifurcation of the reverse process. Through a suite of matched-magnitude controls, we show that the variable on which the model commits is directional, concentrated in a low-rank subspace of the write's perturbation drift. Motivated by this finding, we introduce PowerRemap, a test-time control that reshapes the singular spectrum of the localized write to suppress this drift, with rescue rates of 98.3% on WaLa and 84.6% on Make-a-Shape. Together, these results link a circuit-level cross-attention mechanism to a trajectory-level account of the failure, demonstrating how mechanistic analysis can explain and guide behavior in conditional diffusion transformers.

cs.LG↗

arXiv2025

Shape Generation via Weight Space Learning

Foundation models for 3D shape generation have recently shown a remarkable capacity to encode rich geometric priors across both global and local dimensions. However, leveraging these priors for downstream tasks can be challenging as real-world data are often scarce or noisy, and traditional fine-tuning can lead to catastrophic forgetting. In this work, we treat the weight space of a large 3D shape-generative model as a data modality that can be explored directly. We hypothesize that submanifolds within this high-dimensional weight space can modulate topological properties or fine-grained part features separately, demonstrating early-stage evidence via two experiments. First, we observe a sharp phase transition in global connectivity when interpolating in conditioning space, suggesting that small changes in weight space can drastically alter topology. Second, we show that low-dimensional reparameterizations yield controlled local geometry changes even with very limited data. These results highlight the potential of weight space learning to unlock new approaches for 3D shape generation and specialized fine-tuning.

cs.CV↗