This chapter looks at prediction from the point of view of perception; namely, the fitting or inversion of internal models of sensory data by the brain. It focuses on how neural networks could be configured to invert these models and deconvolve sensory causes from sensory input. The chapter is organized as follows. The first section introduces hierarchical dynamic models. Hierarchies induce empirical priors that provide constraints, which are exploited during inversion. The second considers model inversion in statistical terms. The third shows how this inversion can be formulated as a simple gradient ascent using neuronal networks. The final section considers how evoked brain responses might be understood in terms of inference under hierarchical dynamic models of sensory input.