This paper introduces a novel data-driven strategy for synthesizing gramophone noise audio textures. A diffusion probabilistic model is applied to generate highly realistic quasiperiodic noises. The proposed model is designed to generate samples of length equal to one disk revolution, but a method to generate plausible periodic variations between revolutions is also proposed. A guided approach is also applied as a conditioning method, where an audio signal generated with manually-tuned signal processing is refined via reverse diffusion to improve realism. The method has been evaluated in a subjective listening test, in which the participants were often unable to recognize the synthesized signals from the real ones. The synthetic noises produced with the best proposed unconditional method are statistically indistinguishable from real noise recordings. This work shows the potential of diffusion models for highly realistic audio synthesis tasks.