Apparently, DP has some detractors. I was told by my signal processing professor that differential privacy wasn't really a solution for privacy preserving data analysis. He said something along these lines: "if I know something about the underlying data distribution (Gaussian, etc.), it is possible to wash out the randomness."

Now, I don't understand DP well enough and information theory/signal processing still seems a bit like "dragons be here" to me. But, I want to take a stab at trying to reason why he said that.

For example, take randomized response (the only DP technique I understand). That is vulnerable to a longitudinal attack: a person can query repeatedly to wash out the randomness. If you think about it, isn't it the almost the inverse of a repetition code (error correction)? There, you're trying to use redundancy (repetition) to remove noise.