Seismograms predicted from acoustic or elastic earth models depend very non-linearly on the long wavelength components of velocity. This sensitive dependence demands the use of special variational principles in waveform-based inversion algorithms. The differential semblance variational principle is well-suited to velocity inversion by gradient methods, since its objective function is smooth and convex over a large range of velocity models. An extension of the adjoint state technique yields an accurate estimate of the differential semblance gradient. Non-linear conjugate gradient iteration is quite successful in locating the global differential semblance minimum, which is near the ordinary least-squares global minimum when coherent data noise is small. Several examples, based on the 2D primaries-only acoustic model, illustrate features of the method and its performance.