diff --git a/compiler/rustc_borrowck/src/polonius/liveness_constraints.rs b/compiler/rustc_borrowck/src/polonius/liveness_constraints.rs
new file mode 100644
index 00000000000..6ed13313463
--- /dev/null
+++ b/compiler/rustc_borrowck/src/polonius/liveness_constraints.rs
@@ -0,0 +1,125 @@
+use std::collections::BTreeMap;
+
+use rustc_middle::ty::relate::{self, Relate, RelateResult, TypeRelation};
+use rustc_middle::ty::{self, RegionVid, Ty, TyCtxt, TypeVisitable};
+
+use super::{ConstraintDirection, PoloniusContext};
+use crate::universal_regions::UniversalRegions;
+
+impl PoloniusContext {
+    /// Record the variance of each region contained within the given value.
+    pub(crate) fn record_live_region_variance<'tcx>(
+        &mut self,
+        tcx: TyCtxt<'tcx>,
+        universal_regions: &UniversalRegions<'tcx>,
+        value: impl TypeVisitable<TyCtxt<'tcx>> + Relate<TyCtxt<'tcx>>,
+    ) {
+        let mut extractor = VarianceExtractor {
+            tcx,
+            ambient_variance: ty::Variance::Covariant,
+            directions: &mut self.live_region_variances,
+            universal_regions,
+        };
+        extractor.relate(value, value).expect("Can't have a type error relating to itself");
+    }
+}
+
+/// Extracts variances for regions contained within types. Follows the same structure as
+/// `rustc_infer`'s `Generalizer`: we try to relate a type with itself to track and extract the
+/// variances of regions.
+struct VarianceExtractor<'a, 'tcx> {
+    tcx: TyCtxt<'tcx>,
+    ambient_variance: ty::Variance,
+    directions: &'a mut BTreeMap<RegionVid, ConstraintDirection>,
+    universal_regions: &'a UniversalRegions<'tcx>,
+}
+
+impl<'tcx> VarianceExtractor<'_, 'tcx> {
+    fn record_variance(&mut self, region: ty::Region<'tcx>, variance: ty::Variance) {
+        // We're only interested in the variance of vars and free regions.
+
+        if region.is_bound() || region.is_erased() {
+            // ignore these
+            return;
+        }
+
+        let direction = match variance {
+            ty::Variance::Covariant => ConstraintDirection::Forward,
+            ty::Variance::Contravariant => ConstraintDirection::Backward,
+            ty::Variance::Invariant => ConstraintDirection::Bidirectional,
+            ty::Variance::Bivariant => {
+                // We don't add edges for bivariant cases.
+                return;
+            }
+        };
+
+        let region = self.universal_regions.to_region_vid(region);
+        self.directions
+            .entry(region)
+            .and_modify(|entry| {
+                // If there's already a recorded direction for this region, we combine the two:
+                // - combining the same direction is idempotent
+                // - combining different directions is trivially bidirectional
+                if entry != &direction {
+                    *entry = ConstraintDirection::Bidirectional;
+                }
+            })
+            .or_insert(direction);
+    }
+}
+
+impl<'tcx> TypeRelation<TyCtxt<'tcx>> for VarianceExtractor<'_, 'tcx> {
+    fn cx(&self) -> TyCtxt<'tcx> {
+        self.tcx
+    }
+
+    fn relate_with_variance<T: Relate<TyCtxt<'tcx>>>(
+        &mut self,
+        variance: ty::Variance,
+        _info: ty::VarianceDiagInfo<TyCtxt<'tcx>>,
+        a: T,
+        b: T,
+    ) -> RelateResult<'tcx, T> {
+        let old_ambient_variance = self.ambient_variance;
+        self.ambient_variance = self.ambient_variance.xform(variance);
+        let r = self.relate(a, b)?;
+        self.ambient_variance = old_ambient_variance;
+        Ok(r)
+    }
+
+    fn tys(&mut self, a: Ty<'tcx>, b: Ty<'tcx>) -> RelateResult<'tcx, Ty<'tcx>> {
+        assert_eq!(a, b); // we are misusing TypeRelation here; both LHS and RHS ought to be ==
+        relate::structurally_relate_tys(self, a, b)
+    }
+
+    fn regions(
+        &mut self,
+        a: ty::Region<'tcx>,
+        b: ty::Region<'tcx>,
+    ) -> RelateResult<'tcx, ty::Region<'tcx>> {
+        assert_eq!(a, b); // we are misusing TypeRelation here; both LHS and RHS ought to be ==
+        self.record_variance(a, self.ambient_variance);
+        Ok(a)
+    }
+
+    fn consts(
+        &mut self,
+        a: ty::Const<'tcx>,
+        b: ty::Const<'tcx>,
+    ) -> RelateResult<'tcx, ty::Const<'tcx>> {
+        assert_eq!(a, b); // we are misusing TypeRelation here; both LHS and RHS ought to be ==
+        relate::structurally_relate_consts(self, a, b)
+    }
+
+    fn binders<T>(
+        &mut self,
+        a: ty::Binder<'tcx, T>,
+        _: ty::Binder<'tcx, T>,
+    ) -> RelateResult<'tcx, ty::Binder<'tcx, T>>
+    where
+        T: Relate<TyCtxt<'tcx>>,
+    {
+        self.relate(a.skip_binder(), a.skip_binder())?;
+        Ok(a)
+    }
+}
diff --git a/compiler/rustc_borrowck/src/polonius/mod.rs b/compiler/rustc_borrowck/src/polonius/mod.rs
index 16487de09e2..d86edd00725 100644
--- a/compiler/rustc_borrowck/src/polonius/mod.rs
+++ b/compiler/rustc_borrowck/src/polonius/mod.rs
@@ -36,6 +36,7 @@
 mod constraints;
 mod dump;
 pub(crate) mod legacy;
+mod liveness_constraints;
 
 use std::collections::BTreeMap;