# Stylish and Functional: Guided Interpolation Subject to Physical Constraints

arXiv: https://arxiv.org/abs/2412.15507 · HTML: https://mlsanity.com/paper/2412.15507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 8 of 8)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [Stabilizing Training of Generative Adversarial Networks through Regularization](https://mlsanity.com/paper/1705.09367/) (2017)
- [Interpolating between Images with Diffusion Models](https://mlsanity.com/paper/2307.12560/) (2023)
- [Transferable and Principled Efficiency for Open-Vocabulary Segmentation](https://mlsanity.com/paper/2404.07448/) (2024)

## Abstract (arXiv)

Generative AI is revolutionizing engineering design practices by enabling rapid prototyping and manipulation of designs. One example of design manipulation involves taking two reference design images and using them as prompts to generate a design image that combines aspects of both. Real engineering designs have physical constraints and functional requirements in addition to aesthetic design considerations. Internet-scale foundation models commonly used for image generation, however, are unable to take these physical constraints and functional requirements into consideration as part of the generation process. We consider the problem of generating a design inspired by two input designs, and propose a zero-shot framework toward enforcing physical, functional requirements over the generation process by leveraging a pretrained diffusion model as the backbone. As a case study, we consider the example of rotational symmetry in generation of wheel designs. Automotive wheels are required to be rotationally symmetric for physical stability. We formulate the requirement of rotational symmetry by the use of a symmetrizer, and we use this symmetrizer to guide the diffusion process towards symmetric wheel generations. Our experimental results find that the proposed approach makes generated interpolations with higher realism than methods in related work, as evaluated by Fr'echet inception distance (FID). We also find that our approach generates designs that more closely satisfy physical and functional requirements than generating without the symmetry guidance.