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.

Discovering what is learned by neural networks remains a challenge. In self-supervised learning, classification is the most common task used to evaluate how good a representation is. However, relying only on such downstream task can limit our understanding of how much information is retained in the representation of a given input. In this work, we showcase the use of a conditional diffusion based generative model (RCDM) to visualize representations learned with self-supervised models. We further demonstrate how this model's generation quality is on par with state-of-the-art generative models while being faithful to the representation used as conditioning. By using this new tool to analyze self-supervised models, we can show visually that i) SSL (backbone) representation are not really invariant to many data augmentation they were trained on. ii) SSL projector embedding appear too invariant for tasks like classifications. iii) SSL representations are more robust to small adversarial perturbation of their inputs iv) there is an inherent structure learned with SSL model that can be used for image manipulation.

A non-vector-based dissimilarity measure is proposed by combining vector-based distance metrics and set operations. This proposed compound dissimilarity measure (CDM) is applicable to quantify similarity of collections of attribute/feature pairs where not all attributes are present in all collections. This is a typical challenge in the context of e.g., fingerprinting-based positioning (FbP). Compared to vector-based distance metrics (e.g., Minkowski), the merits of the proposed CDM are i) the data do not need to be converted to vectors of equal dimension, ii) shared and unshared attributes can be weighted differently within the assessment, and iii) additional degrees of freedom within the measure allow to adapt its properties to application needs in a data-driven way. We indicate the validity of the proposed CDM by demonstrating the improvements of the positioning performance of fingerprinting-based WLAN indoor positioning using four different datasets, three of them publicly available. When processing these datasets using CDM instead of conventional distance metrics the accuracy of identifying buildings and floors improves by about 5% on average. The 2d positioning errors in terms of root mean squared error (RMSE) are reduced by a factor of two, and the percentage of position solutions with less than 2m error improves by over 10%.