Planar Symmetric Pattern Generation

Generating objects with specific symmetries is essential in various real-world scenarios. However, adapting existing 2D continuous representations to enforce planar group symmetry remains a challenge, as the transformation of non-reflective group elements may disrupt continuity. To overcome this limitation, we propose a symmetrization framework for arbitrary planar groups. Our method transforms any 2D continuous representation into a symmetric one while preserving continuity. We provide the mathematical formulation of this representation, demonstrate its approximation capability for symmetric functions, and detail the construction methodology. We validate our approach through three visual design tasks (pattern design, paper-cutting design and stylized topology design) and one material design task. Experiments confirm that our representation enables effective symmetry control and demonstrate its broader applicability.

Optimization and Generation in Aerodynamics Inverse Design

Inverse design with physics-based objectives is challenging because it couples high-dimensional geometry with expensive simulations, as exemplified by aerodynamic shape optimization for drag reduction. We revisit inverse design through two canonical solutions, the optimal design point and the optimal design distribution, and relate them to optimization and guided generation. Building on this view, we propose a new training loss for cost predictors and a density-gradient optimization method that improves objectives while preserving plausible shapes. We further unify existing training-free guided generation methods. To address their inability to approximate conditional covariance in high dimensions, we develop a time- and memory-efficient algorithm for approximate covariance estimation. Experiments on a controlled 2D study and high-fidelity 3D aerodynamic benchmarks (car and aircraft), validated by OpenFOAM simulations and miniature wind-tunnel tests with 3D-printed prototypes, demonstrate consistent gains in both optimization and guided generation. Additional offline RL results further support the generality of our approach.

FlexWorld: Progressively Expanding 3D Scenes for Flexiable-View Synthesis

Generating flexible-view 3D scenes, including 360{\deg} rotation and zooming, from single images is challenging due to a lack of 3D data. To this end, we introduce FlexWorld, a novel framework consisting of two key components: (1) a strong video-to-video (V2V) diffusion model to generate high-quality novel view images from incomplete input rendered from a coarse scene, and (2) a progressive expansion process to construct a complete 3D scene. In particular, leveraging an advanced pre-trained video model and accurate depth-estimated training pairs, our V2V model can generate novel views under large camera pose variations. Building upon it, FlexWorld progressively generates new 3D content and integrates it into the global scene through geometry-aware scene fusion. Extensive experiments demonstrate the effectiveness of FlexWorld in generating high-quality novel view videos and flexible-view 3D scenes from single images, achieving superior visual quality under multiple popular metrics and datasets compared to existing state-of-the-art methods. Qualitatively, we highlight that FlexWorld can generate high-fidelity scenes with flexible views like 360{\deg} rotations and zooming. Project page: https://ml-gsai.github.io/FlexWorld.

MicroDreamer: Zero-shot 3D Generation in $\sim$20 Seconds by Score-based Iterative Reconstruction

Optimization-based approaches, such as score distillation sampling (SDS), show promise in zero-shot 3D generation but suffer from low efficiency, primarily due to the high number of function evaluations (NFEs) required for each sample. In this paper, we introduce score-based iterative reconstruction (SIR), an efficient and general algorithm for 3D generation with a multi-view score-based diffusion model. Given the images produced by the diffusion model, SIR reduces NFEs by repeatedly optimizing 3D parameters, unlike the single optimization in SDS, mimicking the 3D reconstruction process. With other improvements including optimization in the pixel space, we present an efficient approach called MicroDreamer that generally applies to various 3D representations and 3D generation tasks. In particular, retaining a comparable performance, MicroDreamer is 5-20 times faster than SDS in generating neural radiance field and takes about 20 seconds to generate meshes from 3D Gaussian splitting on a single A100 GPU, halving the time of the fastest zero-shot baseline, DreamGaussian. Our code is available at https://github.com/ML-GSAI/MicroDreamer.