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Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterations

Kaibo Wang, Jianda Mao, Tong Wu, Yang Xiang

TL;DR

This work proposes a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation, and introduces Foresight Guidance, which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations.

Abstract

Classifier-Free Guidance (CFG) is an essential component of text-to-image diffusion models, and understanding and advancing its operational mechanisms remains a central focus of research. Existing approaches stem from divergent theoretical interpretations, thereby limiting the design space and obscuring key design choices. To address this, we propose a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation. We demonstrate that CFG and its variants constitute a special case of single-step short-interval iteration, which is theoretically proven to exhibit inefficiency. To this end, we introduce Foresight Guidance (FSG), which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations. Extensive experiments across diverse datasets and model architectures validate the superiority of FSG over state-of-the-art methods in both image quality and computational efficiency. Our work offers novel perspectives for conditional guidance and unlocks the potential of adaptive design.

Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterations

TL;DR

This work proposes a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation, and introduces Foresight Guidance, which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations.

Abstract

Classifier-Free Guidance (CFG) is an essential component of text-to-image diffusion models, and understanding and advancing its operational mechanisms remains a central focus of research. Existing approaches stem from divergent theoretical interpretations, thereby limiting the design space and obscuring key design choices. To address this, we propose a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation. We demonstrate that CFG and its variants constitute a special case of single-step short-interval iteration, which is theoretically proven to exhibit inefficiency. To this end, we introduce Foresight Guidance (FSG), which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations. Extensive experiments across diverse datasets and model architectures validate the superiority of FSG over state-of-the-art methods in both image quality and computational efficiency. Our work offers novel perspectives for conditional guidance and unlocks the potential of adaptive design.
Paper Structure (39 sections, 3 theorems, 53 equations, 16 figures, 12 tables, 3 algorithms)

This paper contains 39 sections, 3 theorems, 53 equations, 16 figures, 12 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Diffusion Models
  4. Classifier-Free Guidance
  5. Methodology
  6. Towards the Golden Path via Fixed Point Iterations
  7. Foresight Guidance
  8. Experiments
  9. Experimental Setup
  10. Experimental Results
  11. Related Works
  12. Conclusion
  13. Unified Framework
  14. Classifier-Free Guidance (CFG) [CFG]
  15. CFG++ [CFG++]
  16. ...and 24 more sections

Key Result

Theorem 1

(Detailed in Appendix app:proofs) Let $\mathcal{L}=\frac{1}{T}\sum_{t=1}^T\lVert\epsilon^c(\hat{x}_t)-\epsilon^u(\hat{x}_t)\rVert_2^2$ denote the average gap over calibrated trajectories $\hat{x}_t\in\mathbb{R}^d$, with $B$ as the Euclidean norm bound for $\hat{x}_t$ and $\epsilon^{c/u}(\hat{x}_t)$,

Figures (16)

  • Figure 1: From left to right: (a) Illustration of the golden path. Latents $\hat{x}_t$ generating mountains unconditionally produce higher-quality images when guided by mountain-related prompts. (b) Unified framework for fixed point iterations. The state $x_t$ is calibrated toward $\hat{x}_t$ on the golden path via fixed point iterations. (c) Proposed foresight guidance (FSG). We enhance efficiency and alignment by conducting fixed point iterations over longer intervals with increased iterations.
  • Figure 2: Left: Proportion of samples that outperform the other four methods (Top-1 rate). Right: Prediction gap during denoising, indicating the effectiveness of the fixed point iteration. Dataset: DrawBench, NFE: 50, see Appendix \ref{['app:top1_rate']} and \ref{['app:prediction_gap']} for more results.
  • Figure 3: Results of qualitative analysis. Our proposed FSG demonstrates effectiveness in several dimensions including text, details, and counting. We present more examples in Appendix \ref{['app:visual_results']}.
  • Figure 4: Quantitative results on ImageNet $256\times 256$. Model: DiT.
  • Figure 5: Synergistic effects of FSG and noise optimization model (NPNet) Dataset: Pick-a-Pic.
  • ...and 11 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Theorem : detailed version of \ref{['thm:main']}
  • Lemma 1
  • proof
  • proof