From the formulation of the question, I assume that there are no "examples" of anomalies (i.e. labels) whatsoever. With that assumption, a feasible approach would be to use autoencoders: neural networks that receive as input your data and are trained to output that very same data. The idea is that the training has allowed the net to learn representations of the input data distributions in the form of latent variables.
There is a type of autoencoder called denoising autoencoder, which is trained with corrupted versions of the original data as input and with the uncorrupted original data as output. This delivers a network that can remove noise (i.e. data corruptions) from the inputs.
You may train a denoising autoencoder with the daily data. Then use it on new daily data; this way you have the original daily data and an uncorrupted version of those very same data. You can then compare both to detect significant differences.
The key here is which definition of significant difference you choose. You could compute the euclidean distance and assume that if it surpasses certain arbitrary threshold, you have an anomaly. Another important factor is the kind of corruptions you introduce; they should be as close as possible to reasonable abnormalities.
Another option would be to use Generative Adversarial Networks. The byproduct of the training is a discriminator network that tells apart normal daily data from abnormal data.