Path Probing: In a path probing attack, an attacker intentionally sends payments through the network in an attempt to discover the shape of the network and the distribution of liquidity. This works because the LN responds differently to a payment attempt depending on whether it would succeed or fail due to insufficient capacity in a channel. By repeatedly sending payments of varying sizes along different paths, an attacker can gain information about the distribution of funds in the network's channels. Over time, by correlating this data, an attacker could potentially gain an understanding of the network's structure and where liquidity is concentrated, enabling them to make educated guesses about the paths that real transactions are likely to take.
Timing Analysis: In a timing analysis attack, an adversary would monitor the time taken for transactions to pass through nodes in an attempt to correlate the timing of transactions entering and leaving different parts of the network. Even though the LN does not publicly broadcast transactions as in the base layer of Bitcoin, the timing of transactions can still be observed by malicious nodes. If an adversary runs multiple nodes, they can compare the time when transactions enter and leave their nodes. If they see a match (a transaction entering one node and leaving another with approximately the same amount at approximately the same time), they might be able to link those transactions together.