Data scarcity hinders deep learning for medical imaging. We propose a framework for breast cancer classification in thermograms that addresses this using a Diffusion Probabilistic Model (DPM) for data augmentation. Our DPM-based augmentation is shown to be superior to both traditional methods and a ProGAN baseline. The framework fuses deep features from a pre-trained ResNet-50 with handcrafted nonlinear features (e.g., Fractal Dimension) derived from U-Net segmented tumors. An XGBoost classifier trained on these fused features achieves 98.0\% accuracy and 98.1\% sensitivity. Ablation studies and statistical tests confirm that both the DPM augmentation and the nonlinear feature fusion are critical, statistically significant components of this success. This work validates the synergy between advanced generative models and interpretable features for creating highly accurate medical diagnostic tools.