arXiv:2603.29585v1 Announce Type: cross Abstract: The ability to transform a flat sheet into a complex three-dimensional structure is a fundamental test of physical intelligence. Unlike cloth manipulation, origami is governed by strict geometric axioms and hard kinematic constraints, where a single invalid crease or collision can invalidate the entire folding sequence. As a result, origami demands long-horizon constructive reasoning that jointly satisfies precise physical laws and high-level semantic intent. Existing approaches fall into two disjoint paradigms: optimization-based methods enforce physical validity but require dense, precisely specified inputs, making them unsuitable for sparse natural language descriptions, while generative foundation models excel at semantic and perceptual synthesis yet fail to produce long-horizon, physics-consistent folding processes. Consequently, generating valid origami folding sequences directly from text remains an open challenge. To address this gap, we introduce Learn2Fold, a neuro-symbolic framework that formulates origami folding as conditional program induction over a crease-pattern graph. Our key insight is to decouple semantic proposal from physical verification. A large language model generates candidate folding programs from abstract text prompts, while a learned graph-structured world model serves as a differentiable surrogate simulator that predicts physical feasibility and failure modes before execution. Integrated within a lookahead planning loop, Learn2Fold enables robust generation of physically valid folding sequences for complex and out-of-distribution patterns, demonstrating that effective spatial intelligence arises from the synergy between symbolic reasoning and grounded physical simulation.

arXiv:2603.06741v1 Announce Type: cross Abstract: Training frontier-scale diffusion models often requires substantial computational resources concentrated in tightly coupled clusters, limiting participation to well-resourced institutions. While Decentralized Diffusion Models (DDM) enable training multiple experts in isolation, existing approaches require 1176 GPU-days and homogeneous training objectives across all experts. We present an efficient framework that reduces resource requirements while supporting heterogeneous training objectives. Our approach combines three contributions: (1) a heterogeneous decentralized training paradigm that allows experts to use different objectives (DDPM and Flow Matching), unified at inference time via a deterministic schedule-aware conversion into a common velocity space without retraining; (2) pretrained checkpoint conversion from ImageNet-DDPM to Flow Matching objectives, accelerating convergence and enabling initialization without objective-specific pretraining; and (3) PixArt-alpha's efficient AdaLN-Single architecture, reducing parameters while maintaining quality. Experiments on LAION-Aesthetics show that, relative to the training scale reported for prior DDM work, our approach reduces compute from 1176 to 72 GPU-days (16x) and data from 158M to 11M (14x). Under aligned inference settings, our heterogeneous 2DDPM:6FM configuration achieves better FID (11.88 vs. 12.45) and higher intra-prompt diversity (LPIPS 0.631 vs. 0.617) than the homogeneous 8FM baseline. By eliminating synchronization requirements and enabling mixed DDPM/FM objectives, our framework lowers infrastructure requirements for decentralized generative model training.