  The always-available liquidity of automated market makers (AMMs) has been one
of the most important catalysts in early cryptocurrency adoption. However, it
has become increasingly evident that AMMs in their current form are not viable
investment options for passive liquidity providers. This is large part due to
the cost incurred by AMMs providing stale prices to arbitrageurs against
external market prices, formalized as loss-versus-rebalancing (LVR) [Milionis
et al., 2022].
  In this paper, we present Diamond, an automated market making protocol that
aligns the incentives of liquidity providers and block producers in the
protocol-level retention of LVR. In Diamond, block producers effectively
auction the right to capture any arbitrage that exists between the external
market price of a Diamond pool, and the price of the pool itself. The proceeds
of these auctions are shared by the Diamond pool and block producer in a way
that is proven to remain incentive compatible for the block producer. Given the
participation of competing arbitrageurs to capture LVR, LVR is minimized in
Diamond.
  We formally prove this result, and detail an implementation of Diamond. We
also provide comparative simulations of Diamond to relevant benchmarks, further
evidencing the LVR-protection capabilities of Diamond.
  With this new protection, passive liquidity provision on blockchains can
become rationally viable, beckoning a new age for decentralized finance.
