diff --git a/flows/embedding_flow.py b/flows/embedding_flow.py
index 9ebe7a2..3d638ec 100644
--- a/flows/embedding_flow.py
+++ b/flows/embedding_flow.py
@@ -296,9 +296,16 @@ def embedding_flow(
     reference_speedup: float = 10.0,
     samples: int = 10_000,
 ):
+    # Preserve the user-supplied generator_kwargs for hashing / metadata —
+    # the merged dict (with random_state defaults + n_samples) goes to the
+    # generator itself but those aren't part of the run's semantic identity
+    # (random_state=0 is a flow constant; n_samples is captured as `N` in
+    # the stem). If the merged dict were hashed, the web app would disagree
+    # with the flow because Prefect only records the user-supplied form.
+    user_generator_kwargs = dict(generator_kwargs or {})
     generator_kwargs = {
         **_DEFAULT_GENERATOR_KWARGS,
-        **(generator_kwargs or {}),
+        **user_generator_kwargs,
         "n_samples": num_points,
     }
     embed_columns = (
@@ -311,7 +318,7 @@ def embedding_flow(
     output_ref: str = (
         f"{output_dir.strip('/')}/{_generator}_Reference_N{num_points}_T{num_timesteps}_J{jitter_scale}_s{seed}.html"
     )
-    _args_tag = _run_args_hash(embed_args, generator_kwargs)
+    _args_tag = _run_args_hash(embed_args, user_generator_kwargs)
     output_embed: str = (
         f"{output_dir.strip('/')}/{_generator}_{embedder.split('.')[-1]}_N{num_points}_T{num_timesteps}_J{jitter_scale}_s{seed}_{_args_tag}.html"
     )
@@ -405,7 +412,7 @@ def embedding_flow(
             "jitter_scale": jitter_scale,
             "seed": seed,
             "generator_path": generator_path,
-            "generator_kwargs": generator_kwargs or {},
+            "generator_kwargs": user_generator_kwargs,
             "embedder": embedder,
             "embed_args": merged_embed_args,
         },
@@ -428,7 +435,7 @@ def embedding_flow(
         frames = parse_plotly_run(emb_path_result)
         # Persist generator_kwargs so the server's label enrichment can
         # regenerate the correct dataset variant (swiss_roll vs hole).
-        frames.setdefault("meta", {})["generator_kwargs"] = generator_kwargs or {}
+        frames.setdefault("meta", {})["generator_kwargs"] = user_generator_kwargs
         Path(output_frames).write_text(
             json.dumps(frames, separators=(",", ":")), encoding="utf-8"
         )