diff --git a/crates/polars-time/src/truncate.rs b/crates/polars-time/src/truncate.rs
index 42cbc16645bf..991ce50b547a 100644
--- a/crates/polars-time/src/truncate.rs
+++ b/crates/polars-time/src/truncate.rs
@@ -37,7 +37,7 @@ impl PolarsTruncate for DatetimeChunked {
                     return Ok(self
                         .apply_values(|t| {
                             let remainder = t % every;
-                            t - remainder + every * (remainder < 0) as i64
+                            t - (remainder + every * (remainder < 0) as i64)
                         })
                         .into_datetime(self.time_unit(), time_zone.clone()));
                 } else {
diff --git a/py-polars/polars/expr/datetime.py b/py-polars/polars/expr/datetime.py
index 59e481d2995d..cdf6ccb6516f 100644
--- a/py-polars/polars/expr/datetime.py
+++ b/py-polars/polars/expr/datetime.py
@@ -270,9 +270,8 @@ def truncate(self, every: str | dt.timedelta | Expr) -> Expr:
         │ 2001-01-01 01:00:00 ┆ 2001-01-01 01:00:00 │
         └─────────────────────┴─────────────────────┘
         """
-        if not isinstance(every, pl.Expr):
+        if isinstance(every, dt.timedelta):
             every = parse_as_duration_string(every)
-
         every = parse_into_expression(every, str_as_lit=True)
         return wrap_expr(self._pyexpr.dt_truncate(every))
 
diff --git a/py-polars/polars/series/datetime.py b/py-polars/polars/series/datetime.py
index c65e822e1044..8c8bfb32bad8 100644
--- a/py-polars/polars/series/datetime.py
+++ b/py-polars/polars/series/datetime.py
@@ -1642,7 +1642,7 @@ def offset_by(self, by: str | Expr) -> Series:
         ]
         """
 
-    def truncate(self, every: str | dt.timedelta | Expr) -> Series:
+    def truncate(self, every: str | dt.timedelta | IntoExprColumn) -> Series:
         """
         Divide the date/ datetime range into buckets.
 
diff --git a/py-polars/tests/unit/operations/namespaces/temporal/test_truncate.py b/py-polars/tests/unit/operations/namespaces/temporal/test_truncate.py
index b679d3859a4c..f56d356b0457 100644
--- a/py-polars/tests/unit/operations/namespaces/temporal/test_truncate.py
+++ b/py-polars/tests/unit/operations/namespaces/temporal/test_truncate.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from datetime import date, datetime
+from datetime import date, datetime, timedelta
 from typing import TYPE_CHECKING
 
 import hypothesis.strategies as st
@@ -8,6 +8,7 @@
 from hypothesis import given
 
 import polars as pl
+from polars._utils.convert import parse_as_duration_string
 from polars.testing import assert_series_equal
 
 if TYPE_CHECKING:
@@ -92,3 +93,29 @@ def test_truncate_datetime_w_expression(time_unit: TimeUnit) -> None:
     result = df.select(pl.col("a").dt.truncate(pl.col("b")))["a"]
     assert result[0] == datetime(2020, 1, 1)
     assert result[1] == datetime(2020, 1, 3)
+
+
+def test_pre_epoch_truncate_17581() -> None:
+    s = pl.Series([datetime(1980, 1, 1), datetime(1969, 1, 1, 1)])
+    result = s.dt.truncate("1d")
+    expected = pl.Series([datetime(1980, 1, 1), datetime(1969, 1, 1)])
+    assert_series_equal(result, expected)
+
+
+@given(
+    datetimes=st.lists(
+        st.datetimes(min_value=datetime(1960, 1, 1), max_value=datetime(1980, 1, 1)),
+        min_size=1,
+        max_size=3,
+    ),
+    every=st.timedeltas(
+        min_value=timedelta(microseconds=1), max_value=timedelta(days=1)
+    ).map(parse_as_duration_string),
+)
+def test_fast_path_vs_slow_path(datetimes: list[datetime], every: str) -> None:
+    s = pl.Series(datetimes)
+    # Might use fastpath:
+    result = s.dt.truncate(every)
+    # Definitely uses slowpath:
+    expected = s.dt.truncate(pl.Series([every] * len(datetimes)))
+    assert_series_equal(result, expected)