diff --git a/torax/_src/interpolated_param.py b/torax/_src/interpolated_param.py
index 9e7b176d9..e8794590b 100644
--- a/torax/_src/interpolated_param.py
+++ b/torax/_src/interpolated_param.py
@@ -58,6 +58,9 @@ class InterpolationMode(enum.Enum):
   input greater than x_n.
 
   Options:
+    NONE: No interpolation. Values are zeros everywhere except for the provided
+      points. Should only be used internally, for the rho dimension in
+      InterpolatedVarTimeRho.
     PIECEWISE_LINEAR: Does piecewise-linear interpolation between the values
       provided. See numpy.interp for a longer description of how it works. (This
       uses JAX, but the behavior is the same.)
@@ -65,12 +68,13 @@ class InterpolationMode(enum.Enum):
       x_k+1), the output will be y_k.
   """
 
+  NONE = 'none'
   PIECEWISE_LINEAR = 'piecewise_linear'
   STEP = 'step'
 
 
 InterpolationModeLiteral: TypeAlias = Literal[
-    'step', 'STEP', 'piecewise_linear', 'PIECEWISE_LINEAR'
+    'step', 'STEP', 'piecewise_linear', 'PIECEWISE_LINEAR', 'none', 'NONE'
 ]
 
 
@@ -515,18 +519,60 @@ def __init__(
     self._rho_interpolation_mode = rho_interpolation_mode
     self._time_interpolation_mode = time_interpolation_mode
 
-    sorted_indices = np.array(sorted(values.keys()))
-    rho_norm_interpolated_values = np.stack(
-        [
-            InterpolatedVarSingleAxis(
-                values[t], rho_interpolation_mode
-            ).get_value(rho_norm)
-            for t in sorted_indices
-        ],
-        axis=0,
-    )
+    sorted_times = np.array(sorted(values.keys()))
+    if self._rho_interpolation_mode == InterpolationMode.NONE:
+      # If no rho interpolation is needed, the given rho_norm locations will be
+      # quantized onto the rho_norm grid, and the values are delta functions at
+      # the quantized rho_norm locations.
+
+      # Check that the same rho_norm values are used for all times
+      given_rho_norm_locations = values[sorted_times[0]][0]
+      for t in sorted_times[1:]:
+        if not np.array_equal(values[t][0], given_rho_norm_locations):
+          raise ValueError(
+              'When rho_interpolation_mode is InterpolationMode.NONE, the'
+              'rho_norm locations must be the same for all times.'
+          )
+
+      # Find the index of the closest rho_norm values on the grid to the
+      # requested rho_norm locations for each time.
+      quantized_rho_norm_indices = np.stack(
+          [
+              [
+                  np.argmin(np.abs(rho_norm - given_rho_norm_locations))
+                  # values[t] is a tuple of (rho_norm, values) arrays, so
+                  # values[t][0] is the set of specified rho_norm locations for
+                  # the time t.
+                  for given_rho_norm_locations in values[t][0]
+              ]
+              for t in sorted_times
+          ],
+          axis=0,
+      )
+
+      # Convert to a grid of delta functions of height `values` at the quantized
+      # rho_norm locations.
+      rho_norm_interpolated_values = np.zeros(
+          (len(sorted_times), len(rho_norm)),
+          dtype=jax_utils.get_np_dtype(),
+      )
+      rho_norm_interpolated_values[
+          np.arange(len(sorted_times))[:, None], quantized_rho_norm_indices
+      ] = np.array(
+          [values[t][1] for t in sorted_times], dtype=jax_utils.get_np_dtype()
+      )
+    else:
+      rho_norm_interpolated_values = np.stack(
+          [
+              InterpolatedVarSingleAxis(
+                  values[t], rho_interpolation_mode
+              ).get_value(rho_norm)
+              for t in sorted_times
+          ],
+          axis=0,
+      )
     self._time_interpolated_var = InterpolatedVarSingleAxis(
-        value=(sorted_indices, rho_norm_interpolated_values),
+        value=(sorted_times, rho_norm_interpolated_values),
         interpolation_mode=time_interpolation_mode,
     )
 
diff --git a/torax/_src/torax_pydantic/interpolated_param_2d.py b/torax/_src/torax_pydantic/interpolated_param_2d.py
index 08a60ff9f..c5b6d4be0 100644
--- a/torax/_src/torax_pydantic/interpolated_param_2d.py
+++ b/torax/_src/torax_pydantic/interpolated_param_2d.py
@@ -49,6 +49,7 @@ class Grid1D(model_base.BaseModelFrozen):
   of all faces (including boundary faces). For a grid with N cells, there are
   N+1 faces.
   """
+
   face_centers: pydantic_types.NumpyArray1DSorted
 
   @pydantic.model_validator(mode='before')
@@ -444,6 +445,23 @@ def get_cached_interpolated_param_face_right(
     )
 
 
+class TimeVaryingPoints(TimeVaryingArray):
+  """A TimeVaryingArray that is defined on a fixed set of rho points, without interpolation in rho."""
+
+  rho_interpolation_mode: Literal[interpolated_param.InterpolationMode.NONE] = (
+      interpolated_param.InterpolationMode.NONE
+  )
+
+  @pydantic.model_validator(mode='before')
+  @classmethod
+  def _conform_data(
+      cls, data: interpolated_param.TimeRhoInterpolatedInput | dict[str, Any]
+  ) -> dict[str, Any]:
+    data = super()._conform_data(data)
+    data['rho_interpolation_mode'] = interpolated_param.InterpolationMode.NONE
+    return data
+
+
 def _is_positive(array: TimeVaryingArray) -> TimeVaryingArray:
   for _, value in array.value.values():
     if not np.all(value > 0):
diff --git a/torax/_src/torax_pydantic/tests/interpolated_param_2d_test.py b/torax/_src/torax_pydantic/tests/interpolated_param_2d_test.py
index 9c54361ab..2ae3b32eb 100644
--- a/torax/_src/torax_pydantic/tests/interpolated_param_2d_test.py
+++ b/torax/_src/torax_pydantic/tests/interpolated_param_2d_test.py
@@ -615,6 +615,40 @@ def f(
     np.testing.assert_allclose(cell, [8.0, 10.0, 12.0, 14.0])
     self.assertEqual(jax_utils.get_number_of_compiles(f), 1)
 
+  @parameterized.named_parameters(
+      dict(
+          testcase_name='dict_input',
+          time_rho_interpolated_input={
+              0.0: {0.0: 1.0, 1.0: 2.0},
+              1.0: {0.0: 3.0, 1.0: 4.0},
+          },
+          expected_values={
+              0.0: np.array([1.0, 0.0, 0.0, 2.0]),
+              0.5: np.array([2.0, 0.0, 0.0, 3.0]),
+              1.0: np.array([3.0, 0.0, 0.0, 4.0]),
+          },
+      ),
+      dict(
+          testcase_name='rho_norm_quantization',
+          time_rho_interpolated_input={0.0: {0.5: 1.0}},
+          expected_values={
+              0.0: np.array([0.0, 1.0, 0.0, 0.0]),
+          },
+      ),
+  )
+  def test_time_varying_points(
+      self, time_rho_interpolated_input, expected_values
+  ):
+    tvp = interpolated_param_2d.TimeVaryingPoints.model_validate(
+        time_rho_interpolated_input
+    )
+    face_centers = interpolated_param_2d.get_face_centers(4)
+    grid = interpolated_param_2d.Grid1D(face_centers=face_centers)
+    interpolated_param_2d.set_grid(tvp, grid=grid)
+
+    for t, expected_value in expected_values.items():
+      np.testing.assert_array_equal(tvp.get_value(t), expected_value)
+
 
 if __name__ == '__main__':
   absltest.main()
diff --git a/torax/_src/torax_pydantic/torax_pydantic.py b/torax/_src/torax_pydantic/torax_pydantic.py
index 45a0a82b1..4faa30062 100644
--- a/torax/_src/torax_pydantic/torax_pydantic.py
+++ b/torax/_src/torax_pydantic/torax_pydantic.py
@@ -51,6 +51,7 @@
 BaseModelFrozen = model_base.BaseModelFrozen
 
 TimeVaryingScalar = interpolated_param_1d.TimeVaryingScalar
+TimeVaryingPoints = interpolated_param_2d.TimeVaryingPoints
 TimeVaryingArray = interpolated_param_2d.TimeVaryingArray
 NonNegativeTimeVaryingArray = interpolated_param_2d.NonNegativeTimeVaryingArray
 PositiveTimeVaryingScalar = interpolated_param_1d.PositiveTimeVaryingScalar