Agree that validation criteria of the model depend on its type. For example, to validate the probabilistic model in the form of a probability density function, we must use the criterion for testing the null hypothesis (such as chi-square test, Kolmogorov-Smirnov test, Shapiro-Wilk test and others). For validation of the regression model, we need to use additional criteria (for example, F-test). To validate the stochastic model in the form of stochastic differential equation, we need to use additional criteria too (for example, root mean square error criterion).
Therefore, could you please specify the type of model that is used to generate data?
For validating a model you must choose first a probabilistic distribution. The chi-squared test will allow you check if your data belongs to this distribution. I advise you to start with the Gaussian distribution if you have no a priori knowledge.
I think this book will provide you with many alternatives for performing statistical tests, and with useful explanations:
2006, Kanji, Gopal K., "100 Statistical Tests", Third Edition, Sage Publications.