Validiums are L2 scaling solutions similar to ZK Rollups with a basic difference that they use a separate data availability layer instead of posting rollup data on the execution layer (Ethereum mainnet).
Validiums also use ZK proofs to prove state transition validity to the L1. Similar to ZK Rollups, Validiums post the validity proof on the Ethereum mainnet (execution layer). However, unlike ZK Rollups, they don’t post the rollup transaction data on Ethereum mainnet. Instead, they post the data on a separate data availability layer.
This allows validiums to scale more than ZK Rollups, because they are not limited by data availability bandwidth of Ethereum. However, it also makes them relatively less secure because the user withdrawls from L1 could be restricted if data is not properly made available by the external offchain data availability layer.