  A level generator is a tool that generates game levels from noise. Training a
generator without a dataset suffers from feedback sparsity, since it is
unlikely to generate a playable level via random exploration. A common solution
is shaped rewards, which guides the generator to achieve subgoals towards level
playability, but they consume effort to design and require game-specific domain
knowledge. This paper proposes a novel approach to train generators without
datasets or shaped rewards by learning at multiple level sizes starting from
small sizes and up to the desired sizes. The denser feedback at small sizes
negates the need for shaped rewards. Additionally, the generators learn to
build levels at various sizes, including sizes they were not trained for. We
apply our approach to train recurrent auto-regressive generative flow networks
(GFlowNets) for controllable level generation. We also adapt diversity sampling
to be compatible with GFlowNets. The results show that our generators create
diverse playable levels at various sizes for Sokoban, Zelda, and Danger Dave.
When compared with controllable reinforcement learning level generators for
Sokoban, the results show that our generators achieve better controllability
and competitive diversity, while being 9x faster at training and level
generation.
