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RCDM: Enabling Robustness for Conditional Diffusion Model

Weifeng Xu, Xiang Zhu, Xiaoyong Li

TL;DR

RCDM addresses robustness gaps in conditional diffusion models by introducing a dual-network controller whose weights are dynamically tuned during sampling via control-theoretic principles. The method derives a probabilistic framework that quantifies and mitigates the amplification of fixed input errors through a weight filter, without adding computational overhead. Key contributions include a monotonic-overlap analysis I(w) and a balancing rule w = (n|Δ|)/(2c) − 1/2, with n chosen to satisfy competing constraints; extensive experiments on MNIST and CIFAR-10 demonstrate improved robustness (lower FID) while noting a potential decrease in output diversity. The work provides practical guidance for parameter selection, supports real-time applicability, and supplies open-source resources to enable reproducibility and further exploration of robust diffusion-based generation.

Abstract

The conditional diffusion model (CDM) enhances the standard diffusion model by providing more control, improving the quality and relevance of the outputs, and making the model adaptable to a wider range of complex tasks. However, inaccurate conditional inputs in the inverse process of CDM can easily lead to generating fixed errors in the neural network, which diminishes the adaptability of a well-trained model. The existing methods like data augmentation, adversarial training, robust optimization can improve the robustness, while they often face challenges such as high computational complexity, limited applicability to unknown perturbations, and increased training difficulty. In this paper, we propose a lightweight solution, the Robust Conditional Diffusion Model (RCDM), based on control theory to dynamically reduce the impact of noise and significantly enhance the model's robustness. RCDM leverages the collaborative interaction between two neural networks, along with optimal control strategies derived from control theory, to optimize the weights of two networks during the sampling process. Unlike conventional techniques, RCDM establishes a mathematical relationship between fixed errors and the weights of the two neural networks without incurring additional computational overhead. Extensive experiments were conducted on MNIST and CIFAR-10 datasets, and the results demonstrate the effectiveness and adaptability of our proposed model.

RCDM: Enabling Robustness for Conditional Diffusion Model

TL;DR

RCDM addresses robustness gaps in conditional diffusion models by introducing a dual-network controller whose weights are dynamically tuned during sampling via control-theoretic principles. The method derives a probabilistic framework that quantifies and mitigates the amplification of fixed input errors through a weight filter, without adding computational overhead. Key contributions include a monotonic-overlap analysis I(w) and a balancing rule w = (n|Δ|)/(2c) − 1/2, with n chosen to satisfy competing constraints; extensive experiments on MNIST and CIFAR-10 demonstrate improved robustness (lower FID) while noting a potential decrease in output diversity. The work provides practical guidance for parameter selection, supports real-time applicability, and supplies open-source resources to enable reproducibility and further exploration of robust diffusion-based generation.

Abstract

The conditional diffusion model (CDM) enhances the standard diffusion model by providing more control, improving the quality and relevance of the outputs, and making the model adaptable to a wider range of complex tasks. However, inaccurate conditional inputs in the inverse process of CDM can easily lead to generating fixed errors in the neural network, which diminishes the adaptability of a well-trained model. The existing methods like data augmentation, adversarial training, robust optimization can improve the robustness, while they often face challenges such as high computational complexity, limited applicability to unknown perturbations, and increased training difficulty. In this paper, we propose a lightweight solution, the Robust Conditional Diffusion Model (RCDM), based on control theory to dynamically reduce the impact of noise and significantly enhance the model's robustness. RCDM leverages the collaborative interaction between two neural networks, along with optimal control strategies derived from control theory, to optimize the weights of two networks during the sampling process. Unlike conventional techniques, RCDM establishes a mathematical relationship between fixed errors and the weights of the two neural networks without incurring additional computational overhead. Extensive experiments were conducted on MNIST and CIFAR-10 datasets, and the results demonstrate the effectiveness and adaptability of our proposed model.
Paper Structure (26 sections, 5 theorems, 22 equations, 19 figures, 1 table, 2 algorithms)

This paper contains 26 sections, 5 theorems, 22 equations, 19 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Problem Analysis
  5. Robust Conditional Diffusion Model Framework
  6. Mathematical Modeling
  7. Monotonic Constraint
  8. Function Value Constraint
  9. Experiments and Discussion
  10. Validation on MNIST Dataset
  11. Validation on CIFAR-10 Dataset
  12. Conclusion
  13. Appendix
  14. Conditional Diffusion Model
  15. Experimental Pseudocode
  16. ...and 11 more sections

Key Result

Theorem 3.1

Let $\beta_T=\sqrt{1-\alpha_T}$ and $\overline{\beta}_T=\sqrt{1-\overline{\alpha}_T}$. Due to the inaccuracy of the input data, the error $\Delta$ generated by the neural network during the sampling process can accumulate more than $-\frac{1-a_T}{\sqrt{\overline{\alpha}_T(1-\overline{\alpha}_T)}}\De

Figures (19)

  • Figure 1: The forward and reverse processes of conditional diffusion models.
  • Figure 2: Robust conditional diffusion modeling framework.
  • Figure 3: Discrepancy schematic distribution $O_L$ vs. $O_G$.
  • Figure 4: Reflections of $\Delta= 0.3$ on different parameters $w$. With $w=50$, the model can generate numbers in the presence of errors.
  • Figure 5: Reflections of $\Delta= -0.3$ on different parameters $w$. With $w=50$, the model can generate numbers in the presence of errors.
  • ...and 14 more figures

Theorems & Definitions (10)

  • Theorem 3.1
  • proof
  • Definition 3.1
  • Theorem 3.2
  • proof
  • Lemma 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof