  We present an undirected version of the recently introduced flow-augmentation
technique: Given an undirected multigraph $G$ with distinguished vertices $s,t
\in V(G)$ and an integer $k$, one can in randomized $k^{O(1)} \cdot (|V(G)| +
|E(G)|)$ time sample a set $A \subseteq \binom{V(G)}{2}$ such that the
following holds: for every inclusion-wise minimal $st$-cut $Z$ in $G$ of
cardinality at most $k$, $Z$ becomes a minimum-cardinality cut between $s$ and
$t$ in $G+A$ (i.e., in the multigraph $G$ with all edges of $A$ added) with
probability $2^{-O(k \log k)}$.
  Compared to the version for directed graphs [STOC 2022], the version
presented here has improved success probability ($2^{-O(k \log k)}$ instead of
$2^{-O(k^4 \log k)}$), linear dependency on the graph size in the running time
bound, and an arguably simpler proof.
  An immediate corollary is that the Bi-objective $st$-Cut problem can be
solved in randomized FPT time $2^{O(k \log k)} (|V(G)|+|E(G)|)$ on undirected
graphs.
