## 1 Introduction  
Ultrasonic (UT) non-destructive evaluation (NDE) is used in many applications to establish a fitness-for-service argument for components under test [1]. Its usage is widely established in safety-critical contexts such as aviation and nuclear energy [2]. Despite its usefulness, the manual analysis of UT datasets is costly and time-consuming and there is considerable interest in automating the process. This is true for nuclear energy in particular, as ongoing concerns for the environment have sponsored a renewed interest in nuclear energy production as the emissions-free energy it produces may help in stemming the tide of global warming. In order to enhance the cost-effectiveness of nuclear energy relative to emissions-producing alternatives, nuclear plant owner-operators are investigating the use of statistical learning techniques to reduce the financial impact of necessary but costly UT NDE data analysis. While modern statistical learning methods [3] providing decision support in industrial contexts show great promise, the risk and consequence of failure often prevents their usage in highly regulated safety-critical contexts. It is the failure of such methods to provide guarantees on out-of-distribution performance that most strongly prejudices against their usage in the field where any number of factors may impact or skew the distribution of acquired data away from the training data and perhaps negatively impact performance [4]. Our contribution is to demonstrate a principled usage of a state-of-the-art generative model that trains offline on each dataset independently, and so depends only on the distribution of the data at hand, skirting any dependence on out-of-distribution generalization. We work with generative models based on variational inference that allow us to describe, understand, and proof test performance using probabilistic reasoning that captures the method's rationale in a way that regulators familiar with probabilistic risk assessment might be comfortable with. As shown in Figure 1, we summarize a UT data set of _ascans_ as a time series consisting of the peak amplitude response time of flight for each _ascan_. We express the UT data analysis task, on the time series, in probabilistic terms that relate it to a Conditional Score-Based Diffusion (CSDI) [5] loss function and train a CSDI model to perform the probabilistically specified task. We use the threshold reconstruction error of a Variational Autoencoder trained to encode and decode UT _ascas_ to partition the time series dataset as nominal and anomalous subsets; by ignoring the anomalous subset during training, the dataset distribution is effectively biased towards the nominal distribution. Sampling from the trained model and comparing sampled results to the observed data allows us to identify and quantify deviations from nominal. The CSDI model is a conditional score-based derivative of DPM first introduced in [6] and reformulated in [7; 8]. The CSDI architecture differentiates itself by exhibiting state-of-the-art results for time series data imputation on numerous bench-marks and popular time series performance metrics [5]. We use CSDI to impute or estimate unobserved nominal data in our UT NDE datasets. We investigate opportunities to improve nominal estimates by partitioning training datasets to induce bias towards the nominal distribution. CSDI is based on DiffWave [9], which in turn is based on a U-Net like architecture [10]. U-Nets consist of a symmetric stacked encoder and decoder network; with the encoder a series of down-sampling blocks, and the decoder a series of up-sampling blocks. Skip connections run between the corresponding blocks of the encoder and decoder. CSDI  
Figure 1: _ascans_ as shown plotted in the top-right column record the time-of-flight and amplitude response of UT pulses emitted by a probe and then received again after reflection from the test subject. These data are taken from a UT scan of a calibration fixture, inscribed with notches to simulate flaws of various size.