Well log data constitute a primary source of critical information for quantitative reservoir evaluation; however, acquisition failures, wellbore irregularities, and constraints imposed by the log program often result in missing intervals or varying degrees of discontinuity within the recorded well log curves. In recent years, data-driven predictive paradigms have emerged as an effective and increasingly prevalent avenue for reconstructing incomplete well logs; nevertheless, because the process is modulated by stratified lithological heterogeneity, thin-bed phenomena, abrupt depositional interfaces, and inherent petrophysical and tool-response constraints, the task is more rigorously framed as a conditional imputation problem rather than a naive regression formulation. To address this limitation, we propose Diffusion-IDEA, an entirely new framework for well log reconstruction. The framework employs the observed log curves together with geological priors as conditioning constraints and, leveraging a denoising diffusion probabilistic model, performs conditional reconstruction of the missing segments. Unlike existing diffusion-based methods, we implement three key components within our diffusion model: (ⅰ) Dual Mamba; (ⅱ) Thresholded Cross Attention (TCA); and (ⅲ) an Adaptive Filtering and Interpretation Architecture (IDEA). We apply adaptive filtering to modulate the signal-to-noise ratio (SNR) of the observed log signals, while the Dual Mamba module fuses forward and backward representations to provide robust conditioning information. During decoding, the cross-attention module filters salient associations using a cumulative probability threshold; the final output is explicitly decomposed into trend and frequency components to enhance interpretability. Experimental results demonstrate that the proposed model significantly outperforms all existing baselines across every evaluation metric. Compared with the strongest competing method, Diffusion-IDEA achieves state-of-the-art (SOTA) performance, with a relative reduction in MAPE of approximately 22% to 58% across various well-logging parameters.