  Accurately estimating the mixed oil length plays a big role in the economic
benefit for oil pipeline network. While various proposed methods have tried to
predict the mixed oil length, they often exhibit an extremely high probability
(around 50\%) of underestimating it. This is attributed to their failure to
consider the statistical variability inherent in the estimated length of mixed
oil. To address such issues, we propose to use the conditional diffusion model
to learn the distribution of the mixed oil length given pipeline features.
Subsequently, we design a confidence interval estimation for the length of the
mixed oil based on the pseudo-samples generated by the learned diffusion model.
To our knowledge, we are the first to present an estimation scheme for
confidence interval of the oil-mixing length that considers statistical
variability, thereby reducing the possibility of underestimating it. When
employing the upper bound of the interval as a reference for excluding the
mixed oil, the probability of underestimation can be as minimal as 5\%, a
substantial reduction compared to 50\%. Furthermore, utilizing the mean of the
generated pseudo samples as the estimator for the mixed oil length enhances
prediction accuracy by at least 10\% compared to commonly used methods.
