I am a bit confused about what the implication of "no-arbitrage" in popular term struchture models (such as affine term struchtre models or HJM models) are?

Is it solely a restriction on the cross-section of bonds/yields in the sense that at time $t$ arbitrage oppurtunities are excluded or does it also provide a restriction on the time series dimension of bonds/yields? I am confused since e.g. the HJM model provides a dynamic equation for the evolution of forward rates through time and I am unsure if this only implies that for each point in time $t$ oppurtunities are excluded or does it also imply that the dynamic evolution of bonds/yields cohere such that arbitrage oppurtunities are excluded?