Lorenzo Olearo

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures. 3D shapes are represented as the probability distribution induced by a continuous and invertible flow mapping from a fixed anchor distribution. Given a source and a target shape, the composition of the inverse flow (source to anchor) with the forward flow (anchor to target), we continuously map points between the two surfaces. By encoding the shapes with a pointwise task-tailored embedding, this construction provides an invertible and modality-agnostic representation of maps between shapes across point clouds, meshes, signed distance fields (SDFs), and volumetric data. The resulting representation consistently achieves high coverage and accuracy across diverse benchmarks and challenging settings in shape matching. Beyond shape matching, our framework shows promising results in other tasks, including UV mapping and registration of raw point cloud scans of human bodies.

Diffusion models have dramatically advanced text-to-image generation in recent years, translating abstract concepts into high-fidelity images with remarkable ease. In this work, we examine whether they can also blend distinct concepts, ranging from concrete objects to intangible ideas, into coherent new visual entities under a zero-shot framework. Specifically, concept blending merges the key attributes of multiple concepts (expressed as textual prompts) into a single, novel image that captures the essence of each concept. We investigate four blending methods, each exploiting different aspects of the diffusion pipeline (e.g., prompt scheduling, embedding interpolation, or layer-wise conditioning). Through systematic experimentation across diverse concept categories, such as merging concrete concepts, synthesizing compound words, transferring artistic styles, and blending architectural landmarks, we show that modern diffusion models indeed exhibit creative blending capabilities without further training or fine-tuning. Our extensive user study, involving 100 participants, reveals that no single approach dominates in all scenarios: each blending technique excels under certain conditions, with factors like prompt ordering, conceptual distance, and random seed affecting the outcome. These findings highlight the remarkable compositional potential of diffusion models while exposing their sensitivity to seemingly minor input variations.