diff --git a/src/spikeinterface/core/generate.py b/src/spikeinterface/core/generate.py
index 1470473fe2..4fa68ebec0 100644
--- a/src/spikeinterface/core/generate.py
+++ b/src/spikeinterface/core/generate.py
@@ -1072,6 +1072,22 @@ def synthetize_spike_train_bad_isi(duration, baseline_rate, num_violations, viol
     return spike_train
 
 
+def synthesize_amplitude_factor(
+    num_spikes: int,
+    amplitude_factor: np.ndarray | None = None,
+    amplitude_std: float | None = None,
+    seed: np.random.Generator | int | None = None,
+):
+    if amplitude_factor is not None:
+        assert amplitude_factor.shape == (num_spikes,)
+        return amplitude_factor
+    elif amplitude_std:
+        rng = np.random.default_rng(seed)
+        return rng.normal(loc=1, scale=amplitude_std, size=num_spikes)
+    else:
+        return None
+
+
 from spikeinterface.core.basesorting import BaseSortingSegment, BaseSorting
 
 
diff --git a/src/spikeinterface/generation/drifting_generator.py b/src/spikeinterface/generation/drifting_generator.py
index 5529c56a4f..f15d290864 100644
--- a/src/spikeinterface/generation/drifting_generator.py
+++ b/src/spikeinterface/generation/drifting_generator.py
@@ -18,6 +18,7 @@
     generate_unit_locations,
     generate_sorting,
     generate_templates,
+    synthesize_amplitude_factor,
     _ensure_unit_params,
     _ensure_seed,
 )
@@ -366,6 +367,8 @@ def generate_drifting_recording(
     generate_sorting_kwargs=dict(firing_rates=(2.0, 8.0), refractory_period_ms=4.0),
     noise=None,
     generate_noise_kwargs=dict(noise_levels=(6.0, 8.0), spatial_decay=25.0),
+    amplitude_std: float | None = None,
+    amplitude_factor: np.ndarray | None = None,
     extra_outputs=False,
     seed=None,
 ):
@@ -405,6 +408,11 @@ def generate_drifting_recording(
         Noise generator used to generate background noise
     generate_noise_kwargs : dict
         Parameters given to generate_noise() if no noise is None
+    amplitude_std : float, default: 0.05
+        The standard deviation of the modulation to apply to the spikes when injecting them
+        into the recording.
+    amplitude_factor: np.ndarray, optional
+        Optional fixed per-spike amplitude modulation
     extra_outputs : bool, default False
         Return optionaly a dict with more variables.
     seed : None ot int
@@ -559,6 +567,13 @@ def generate_drifting_recording(
         assert noise.probe.get_contact_count() == probe.get_contact_count(), "Noise num channels mismatch"
         assert noise.get_total_duration() == duration, "Noise duration should be the same as the recording duration"
 
+    amplitude_factor = synthesize_amplitude_factor(
+        num_spikes=sorting.count_total_num_spikes(),
+        amplitude_factor=amplitude_factor,
+        amplitude_std=amplitude_std,
+        seed=seed,
+    )
+
     static_recording = InjectDriftingTemplatesRecording(
         sorting=sorting,
         parent_recording=noise,
@@ -567,7 +582,7 @@ def generate_drifting_recording(
         displacement_sampling_frequency=displacement_sampling_frequency,
         displacement_unit_factor=np.zeros_like(displacement_unit_factor),
         num_samples=[int(duration * sampling_frequency)],
-        amplitude_factor=None,
+        amplitude_factor=amplitude_factor,
     )
 
     drifting_recording = InjectDriftingTemplatesRecording(
@@ -578,7 +593,7 @@ def generate_drifting_recording(
         displacement_sampling_frequency=displacement_sampling_frequency,
         displacement_unit_factor=displacement_unit_factor,
         num_samples=[int(duration * sampling_frequency)],
-        amplitude_factor=None,
+        amplitude_factor=amplitude_factor,
     )
 
     if extra_outputs:
diff --git a/src/spikeinterface/generation/hybrid_tools.py b/src/spikeinterface/generation/hybrid_tools.py
index 2476bc6336..244575aff2 100644
--- a/src/spikeinterface/generation/hybrid_tools.py
+++ b/src/spikeinterface/generation/hybrid_tools.py
@@ -10,6 +10,7 @@
     generate_sorting,
     InjectTemplatesRecording,
     _ensure_seed,
+    synthesize_amplitude_factor,
 )
 from spikeinterface.core.template_tools import get_template_extremum_channel
 
@@ -327,6 +328,7 @@ def generate_hybrid_recording(
     upsample_factor: int | None = None,
     upsample_vector: np.ndarray | None = None,
     amplitude_std: float = 0.05,
+    amplitude_factor: np.ndarray | None = None,
     generate_sorting_kwargs: dict = dict(num_units=10, firing_rates=15, refractory_period_ms=4.0, seed=2205),
     generate_unit_locations_kwargs: dict = dict(margin_um=10.0, minimum_z=5.0, maximum_z=50.0, minimum_distance=20),
     generate_templates_kwargs: dict = dict(ms_before=1.0, ms_after=3.0),
@@ -499,10 +501,12 @@ def generate_hybrid_recording(
             upsample_factor = templates_array.shape[3]
             upsample_vector = rng.integers(0, upsample_factor, size=num_spikes)
 
-    if amplitude_std is not None:
-        amplitude_factor = rng.normal(loc=1, scale=amplitude_std, size=num_spikes)
-    else:
-        amplitude_factor = None
+    amplitude_factor = synthesize_amplitude_factor(
+        num_spikes,
+        amplitude_factor=amplitude_factor,
+        amplitude_std=amplitude_std,
+        seed=rng,
+    )
 
     if motion is not None:
         assert num_segments == motion.num_segments, "recording and motion should have the same number of segments"