Patterns of biological diversity across the tree of life are the result of millions of years of evolutionary history and are shaped by natural selection. A long-standing proposal is that most morphological diversity among species arises along "an evolutionary line of least resistance", where new phenotypes arise primarily by elaboration - evolution along this line of least resistance. At macro and mega-evolutionary scales, however, we frequently observe major shifts in phenotypes among lineages. The presence of distinct morphological forms suggests instead that diversity can arise via innovation - where species evolve away from the line of least resistance. Here we apply new multi-trait methods to evaluate the magnitude and distribution of elaboration and innovation in the evolution of bird beaks. Our analyses show that elaboration is a common feature at all scales, consistent with theory. We also find that innovation is a common and major contributor to avian morphological diversity among clades. Furthermore, we show that these patterns of innovation are replicated hierarchically throughout avian evolutionary history. These results suggest that both elaboration and innovation are ubiquitous from macro- to mega-evolutionary scales, and that macroevolutionary axes of multivariate evolution are frequently reoriented throughout the history of life, opening up new avenues for evolution to explore.