One thing to note is that there has been a systematic divergence between the implicit GDP deflator and the CPI (this is noted, e.g., by a 2012 article in Slate by Yglesias[1]). More generally, inflation is always measured using a basket of goods (and services) but there is no guarantee that a specific basket you're using for one purpose is suitable for any other.

[1]: https://slate.com/business/2012/08/the-price-index-divergenc...