diff --git a/diffrax/global_interpolation.py b/diffrax/global_interpolation.py
index 5900bb45..d38f49e2 100644
--- a/diffrax/global_interpolation.py
+++ b/diffrax/global_interpolation.py
@@ -11,7 +11,7 @@
 
 from .custom_types import Array, DenseInfos, Int, PyTree, Scalar
 from .local_interpolation import AbstractLocalInterpolation
-from .misc import fill_forward, left_broadcast_to
+from .misc import fill_forward, left_broadcast_to, linear_rescale
 from .path import AbstractPath
 
 
@@ -124,10 +124,10 @@ def _index(_ys):
         next_ys = (self.ys**ω)[index + 1].ω
         prev_t = self.ts[index]
         next_t = self.ts[index + 1]
-        diff_t = next_t - prev_t
-
         return (
-            prev_ys**ω + (next_ys**ω - prev_ys**ω) * (fractional_part / diff_t)
+            prev_ys**ω
+            + (next_ys**ω - prev_ys**ω)
+            * (linear_rescale(prev_t, fractional_part, next_t))
         ).ω
 
     @eqx.filter_jit
@@ -407,7 +407,6 @@ def _linear_interpolation_forward(
     Tuple[Array["channels":...], Array["channels":...]],  # noqa: F821
     Array["channels":...],  # noqa: F821
 ]:
-
     prev_ti, prev_yi = carry
     ti, yi, next_ti, next_yi = value
     cond = jnp.isnan(yi)
@@ -426,7 +425,6 @@ def _linear_interpolation(
     ys: Array["times", "channels":...],  # noqa: F821
     replace_nans_at_start: Optional[Array["channels":...]] = None,  # noqa: F821
 ) -> Array["times", "channels":...]:  # noqa: F821
-
     ts = left_broadcast_to(ts, ys.shape)
 
     if replace_nans_at_start is None:
@@ -599,7 +597,6 @@ def _hermite_forward(
         Array["channels":...],  # noqa: F821
     ],
 ]:
-
     prev_ti, prev_yi, prev_deriv_i = carry
     ti, yi, next_ti, next_yi = value
     first_deriv_i = (next_yi - yi) / (next_ti - ti)