ABSTRACT Denoising diffusion probabilistic models have emerged as powerful generative frameworks capable of synthesizing high quality images through iterative denoising of Gaussian noise. However, their unconditional nature limits their effectiveness in inverse problems such as denoising, where reconstruction from a specific observation is required. Recent extensions like denoising diffusion restoration models introduce conditional generation by incorporating known degradation operators and pre‐trained denoisers, but these approaches remain heavily reliant on supervised training and large‐scale external datasets. This work proposes a fully unsupervised alternative called the sinusoidal representation network (SIREN)‐guided diffusion denoising model, which integrates implicit neural representations into the diffusion process. We replace the conventional pre‐trained denoiser with a coordinate‐based network (SIREN) optimized directly at inference time. Instead of assuming an explicit degradation model, we perform partial noise injection to the observed signal and initialize the reverse diffusion from this intermediate state. At each step, the SIREN is trained to match the current sample. This integration brings out the complementary strengths of both components: the diffusion process provides a structured, probabilistic coarse‐to‐fine regularization mechanism that stabilizes the optimization trajectory. At the same time, SIREN offers a powerful inductive bias for capturing structured, continuous signals. Crucially, this significantly eliminates the need for early stopping, a known challenge in SIREN‐based denoising, and makes the method highly robust to noise without supervision or clean training data. We evaluate our approach on synthetic and real seismic datasets and demonstrate that it achieves better denoising performance compared to traditional and deep learning‐based baselines.
Li et al. (Fri,) studied this question.