diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 0f18a1fd81815..999dee83cf7e0 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -66,6 +66,7 @@ Other enhancements
 - :class:`Styler` may now render CSS more efficiently where multiple cells have the same styling (:issue:`30876`)
 - When writing directly to a sqlite connection :func:`to_sql` now supports the ``multi`` method (:issue:`29921`)
 - `OptionError` is now exposed in `pandas.errors` (:issue:`27553`)
+- :func:`timedelta_range` will now infer a frequency when passed ``start``, ``stop``, and ``periods`` (:issue:`32377`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_testing.py b/pandas/_testing.py
index fce06e216dfd7..b0f18cb6fdd39 100644
--- a/pandas/_testing.py
+++ b/pandas/_testing.py
@@ -742,9 +742,9 @@ def repr_class(x):
             raise_assert_detail(obj, msg, repr_class(left), repr_class(right))
 
 
-def assert_attr_equal(attr, left, right, obj="Attributes"):
+def assert_attr_equal(attr: str, left, right, obj: str = "Attributes"):
     """
-    checks attributes are equal. Both objects must have attribute.
+    Check attributes are equal. Both objects must have attribute.
 
     Parameters
     ----------
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 81fc934748d3e..749489a0a04fb 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -39,6 +39,7 @@
 from pandas.core.algorithms import checked_add_with_arr
 from pandas.core.arrays import datetimelike as dtl
 import pandas.core.common as com
+from pandas.core.construction import extract_array
 
 from pandas.tseries.frequencies import to_offset
 from pandas.tseries.offsets import Tick
@@ -141,8 +142,7 @@ def dtype(self):
     # Constructors
 
     def __init__(self, values, dtype=_TD_DTYPE, freq=None, copy=False):
-        if isinstance(values, (ABCSeries, ABCIndexClass)):
-            values = values._values
+        values = extract_array(values)
 
         inferred_freq = getattr(values, "_freq", None)
 
@@ -258,6 +258,10 @@ def _generate_range(cls, start, end, periods, freq, closed=None):
             index = _generate_regular_range(start, end, periods, freq)
         else:
             index = np.linspace(start.value, end.value, periods).astype("i8")
+            if len(index) >= 2:
+                # Infer a frequency
+                td = Timedelta(index[1] - index[0])
+                freq = to_offset(td)
 
         if not left_closed:
             index = index[1:]
@@ -614,6 +618,10 @@ def __floordiv__(self, other):
             if self.freq is not None:
                 # Note: freq gets division, not floor-division
                 freq = self.freq / other
+                if freq.nanos == 0 and self.freq.nanos != 0:
+                    # e.g. if self.freq is Nano(1) then dividing by 2
+                    #  rounds down to zero
+                    freq = None
             return type(self)(result.view("m8[ns]"), freq=freq)
 
         if not hasattr(other, "dtype"):
diff --git a/pandas/tests/indexes/timedeltas/test_timedelta_range.py b/pandas/tests/indexes/timedeltas/test_timedelta_range.py
index 9f12af9a96104..c07a6471c732f 100644
--- a/pandas/tests/indexes/timedeltas/test_timedelta_range.py
+++ b/pandas/tests/indexes/timedeltas/test_timedelta_range.py
@@ -38,6 +38,7 @@ def test_linspace_behavior(self, periods, freq):
         result = timedelta_range(start="0 days", end="4 days", periods=periods)
         expected = timedelta_range(start="0 days", end="4 days", freq=freq)
         tm.assert_index_equal(result, expected)
+        assert result.freq == freq
 
     def test_errors(self):
         # not enough params