Quantization offers a practical path to deploying diffusion models with reduced memory and computation, but aggressive compression can cause quantized outputs to deviate substantially from their full-precision counterparts. Sampling-stage correction methods seek to compensate for such deviations during sampling, but existing approaches rely primarily on local information and underexploit trajectory history, limiting their ability to correct errors that propagate across timesteps. In this work, we formulate sampling with a quantized denoiser as an online estimation problem, using the history of quantized denoiser outputs to recover the underlying full-precision outputs required by the sampler. We propose QuAKE, a Quantization-Aware Kalman Estimator that combines a smooth trajectory prior with a conditional Gaussian observation model. At each sampling step, QuAKE recursively updates the posterior over the output window in closed form and feeds its posterior mean to the sampler. QuAKE is a lightweight plug-and-play corrector that requires no modification to the quantized network and naturally supports arbitrary high-order multistep ODE samplers. Experiments across W4A4-quantized text-to-image diffusion models show that QuAKE consistently outperforms existing methods in reducing the distributional discrepancy from full-precision sampling.

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