Stylish and Functional: Guided Interpolation Subject to Physical Constraints

TL;DR

This work tackles generating design interpolations that respect functional constraints by introducing FIT, a zero-shot framework that regularizes diffusion-based latent interpolations with symmetry-based constraints. By applying per-step functional regularization (RA and SS) and a decaying projection during DDIM denoising, FIT improves realism (lower FID) and functional conformance (higher symmetry scores) compared to a baseline interpolation model. The approach balances constraint adherence with visual realism and demonstrates applicability to engineering designs, using rotational symmetry in wheel generation as a concrete case study. The results suggest broad potential for zero-shot constraint-guided interpolation in design workflows, with future work extending to additional physical constraints and domain-specific surrogates.

Abstract

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 Fréchet 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.

Figures (5)

• Figure 1: System overview: The proposed model takes a pair of reference images as the input and generates an intermediate interpolation, where the interpolation is gradually regularized with functional constraints in each step of the denoising process.
• Figure 2: Generating a interpolated combination of two different image sources can create distortion that poses critical challenges to engineering functionality. For example, the distorted spokes are not rotationally symmetrical and hence may distribute force unevenly and affect smooth rolling.
• Figure 3: FID and symmetry score of the generated images over different weight of symmetry (w) in Eq. \ref{['eq:weighting']} that adjusts the impact from the regularization.
• Figure 4: Examples of images generated by the baseline wang2023interpolating (top row) and FIT (bottom row).
• Figure 5: Example images generated by FIT (RA): Left: Applying the constraint during interpolation generation. Right: Applying the constraint at the end of interpolation.