A few times I came across the statement that an Inverted Gamma (3, 0.0005) prior for the variance is quite diffuse but proper. Hence, my understanding is that the prior variance of this random variable is large. However, Wikipedia says that the variance with these parameters equals 0.2500e-04, which is tiny. Indeed, when I sample 1000 draws from this distribution, the standard deviation across draws equals 0.00028099. Similarly, evaluating the cdf at, say, 0.5 yields 1, which means that values larger than 0.5 are very unlikely.
Why is this prior considered diffuse nevertheless?