Stability/consistency issues with Tensorflow sts predictions

Hi,
I have noticed that the predictions with the sts package are sometimes inconsistent over multiple runs, especially when the model is fit with a variational inference surrogate. Running the same code twice can translate into a high accuracy difference. I know that VI find a "local" optimum of the ELBO, and I suppose that running the code twice should obviously lead to slightly different results. However, the observed differences are disturbing when you think of putting your model in production based on these figures. I was wondering if this is a known issue or if it has to do with my model's specification.
Also, for the same model, I run sometimes into the following error:
InvalidArgumentError: Cholesky decomposition was not successful. The input might not be valid. [Op:Cholesky]
running the same code a second time solves apparently the issue but I still don't understand why it works sometimes and sometimes not. Furthermore, may I ask how and when is the Cholesky decomposition used with a VI pipeline?

Platform:

• Tensorflow 2.4
• Tensorflow Probability 0.12.1
• Python 3.6

Thank you for your help,

The issue names no repository files, tests, or reproducible model. Start by reproducing the STS variational-inference behavior with TensorFlow 2.4 and TensorFlow Probability 0.12.1, then trace where the Cholesky operation is reached. Done would require a confirmed cause or a minimal reproducible case that maintainers can investigate.