When random experiments are conducted, 'baseline data' are usually used as control variables in order to increase precision.
How about control variables in Difference in Difference method? What I mean is whether baseline data(Time 1) should be used for it or just control variables at that time(Time 1, Time 2) should be used.
You should use control variables that are available in both periods. As long as they are not themselves outcomes of the treatment (so-called bad controls) you can and should include covariates. For a discussion about as to why see here. In this case controls help with identification. If you use information from time 1 only you can support the common pre-treatment trends assumption. But without time 2 information you may over- or underestimate the treatment effect if your control also changes in period 2 (not because of the treatment but because it varies this way) and affects the outcome.
The other reason to include controls is to soak up some of the residual variance such that statistical tests on your treatment effect have more power. Having covariates for both periods helps with this.
