Goal-conditioned planning benefits from learned low-dimensional representations of rich observations. While compact latent representations typically learned from variational autoencoders or inverse dynamics enable goal-conditioned decision making, they ignore state reachability, hampering their performance. In this paper, we learn a representation that associates reachable states together for effective planning and goal-conditioned policy learning. We first learn a latent representation with multi-step inverse dynamics (to remove distracting information), and then transform this representation to associate reachable states together in $\ell_2$ space. Our proposals are rigorously tested in various simulation testbeds. Numerical results in reward-based settings show significant improvements in sampling efficiency. Further, in reward-free settings this approach yields layered state abstractions that enable computationally efficient hierarchical planning for reaching ad hoc goals with zero additional samples.