Ultrasound videos suffer from hardware-constrained spatial resolution and signal-dependent speckle, while paired low- and high-resolution acquisitions are rarely available. We propose UltraDiff, a self-supervised framework for joint ultrasound video super-resolution and despeckling that uses a frozen pre-trained diffusion model as a plug-in prior. Rather than retraining the model, UltraDiff restores each frame by optimizing the sampler's latent seed under a range-constrained maximum a posteriori-inspired formulation. We derive a speckle-aware data-fidelity term from a Rayleigh scale-family model and characterize its relative-residual and locally variance-adaptive weighting properties. To address degeneracy near zero intensities, we introduce a stabilized surrogate fidelity that is bounded below and strictly convex in log intensity for positive observations in its unclamped form. Total-variation regularization complements the removal of mixed noise, and a temporal seed update warm-starts each frame from the optimized seed of its predecessor, accelerating the convergence. On EchoNet-LVH with simulated speckle and additive noise, UltraDiff with a natural-image prior improves peak signal-to-noise ratio by 1.24\,dB over the strongest baseline, and ultrasound-related priors yield further gains. On 100 real EchoNet-Dynamic videos, UltraDiff reduces the mean absolute error of zero-shot ejection fraction prediction from 7.31 to 6.37 percentage points compared with DUP. These results support ground-truth-free ultrasound video restoration using frozen diffusion priors and a speckle-aware fidelity, without paired training data or model retraining.

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