A Note on Semantic Diffusion

TL;DR

This work addresses the lack of guaranteed convergence in iterative design generation by proposing semantic diffusion, an adaptive semantic layer that overlays a local variation space on top of LLM outputs. It formalizes a fuzzy iterative search over a set of local design variants, using three triangular membership functions for modification intensities and a defuzzified step size to drive convergent refinement. The authors prove convergence and analyze computational complexity for the basic algorithm, and extend the approach with a robust error-tolerant variant that preserves convergence under bounded user mistakes. Empirical-style analysis compares against binary search, showing favorable performance in many settings, and demonstrates practical applicability to guided, incremental design refinement. Overall, the hybrid LLM + semantic diffusion framework offers a principled, controllable path for localized design iteration with formal guarantees.

Abstract

This paper provides an in-depth examination of the concept of semantic diffusion as a complementary instrument to large language models (LLMs) for design applications. Conventional LLMs and diffusion models fail to induce a convergent, iterative refinement process: each invocation of the diffusion mechanism spawns a new stochastic cycle, so successive outputs do not relate to prior ones and convergence toward a desired design is not guaranteed. The proposed hybrid framework - "LLM + semantic diffusion" - resolves this limitation by enforcing an approximately convergent search procedure, thereby formally addressing the problem of localized design refinement.

Figures (7)

• Figure 2: Membership functions for the three intensity levels.
• Figure 3: Analysis of two consecutive queries.
• Figure 4: Handling two consecutive inputs with the same direction.
• Figure 5: Two most recent inputs with opposing directions.
• Figure 6: Case analysis for Group 1.