diff --git a/README.md b/README.md
index 944094c..bbf0a45 100644
--- a/README.md
+++ b/README.md
@@ -85,4 +85,13 @@ sampled_actions = model(vision, commands, joint_state, trajectory_length = 32) #
 }
 ```
 
+```bibtex
+@inproceedings{Sadat2024EliminatingOA,
+    title   = {Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models},
+    author  = {Seyedmorteza Sadat and Otmar Hilliges and Romann M. Weber},
+    year    = {2024},
+    url     = {https://api.semanticscholar.org/CorpusID:273098845}
+}
+```
+
 [*dear alice*](https://www.youtube.com/watch?v=z-Ng5ZvrDm4)
diff --git a/pi_zero_pytorch/pi_zero.py b/pi_zero_pytorch/pi_zero.py
index 47277d4..5b33e7d 100644
--- a/pi_zero_pytorch/pi_zero.py
+++ b/pi_zero_pytorch/pi_zero.py
@@ -11,6 +11,7 @@
 import torch.nn.functional as F
 from torch import pi, nn, tensor, is_tensor
 from torch.nn import Module, ModuleList
+from torch.utils._pytree import tree_map, tree_flatten, tree_unflatten
 
 from torchdiffeq import odeint
 
@@ -91,6 +92,9 @@ def default(v, d):
 
 # tensor helpers
 
+def l2norm(t, dim = -1):
+    return F.normalize(t, dim = dim)
+
 def softclamp(t, value):
     if value <= 0.:
         return t
@@ -110,6 +114,36 @@ def inverse(out, inv_pattern = None):
 
     return packed, inverse
 
+def pack_one_with_inverse(t, pattern):
+    packed, inverse = pack_with_inverse([t], pattern)
+
+    def inverse_one(out, inv_pattern = None):
+        out, = inverse(out, inv_pattern)
+        return out
+
+    return packed, inverse_one
+
+def tree_flatten_with_inverse(input):
+    out, tree_spec = tree_flatten(input)
+
+    def inverse(output):
+        return tree_unflatten(output, tree_spec)
+
+    return out, inverse
+
+def project(x, y):
+    x, inverse = pack_one_with_inverse(x, 'b *')
+    y, _ = pack_one_with_inverse(y, 'b *')
+
+    dtype = x.dtype
+    x, y = x.double(), y.double()
+    unit = l2norm(y, dim = -1)
+
+    parallel = (x * unit).sum(dim = -1, keepdim = True) * unit
+    orthogonal = x - parallel
+
+    return inverse(parallel).to(dtype), inverse(orthogonal).to(dtype)
+
 def pad_at_dim(
     t,
     pad: tuple[int, int],
@@ -556,7 +590,11 @@ def sample(
         trajectory_length: int,
         reward_tokens = None,
         steps = 18,
-        show_pbar = True
+        show_pbar = True,
+        cond_scale = 0.,
+        remove_parallel_component = True,
+        keep_parallel_frac = 0.,
+        cache_kv = True
     ):
         batch_size = token_ids.shape[0]
 
@@ -568,22 +606,31 @@ def sample(
         # ode step function
 
         cached_state_kv = None
+        null_cached_state_kv = None
 
         def ode_fn(timestep, denoised_actions):
             nonlocal cached_state_kv
+            nonlocal null_cached_state_kv
 
-            flow, cached_state_kv = self.forward(
+            flow, (new_cached_state_kv, new_null_cached_state_kv) = self.forward_with_reward_cfg(
                 images,
                 token_ids,
                 joint_states,
                 denoised_actions,
                 times = timestep,
                 reward_tokens = reward_tokens,
-                cached_state_keys_values = cached_state_kv,
+                cached_state_keys_values = (cached_state_kv, null_cached_state_kv),
+                cond_scale = cond_scale,
+                remove_parallel_component = remove_parallel_component,
+                keep_parallel_frac = keep_parallel_frac,
                 return_actions_flow = True,
                 return_state_keys_values = True
             )
 
+            if cache_kv:
+                cached_state_kv = new_cached_state_kv
+                null_cached_state_kv = new_null_cached_state_kv
+
             pbar.update(1)
 
             return flow
@@ -608,24 +655,56 @@ def ode_fn(timestep, denoised_actions):
 
         return sampled_actions
 
+    @torch.no_grad()
     def forward_with_reward_cfg(
         self,
         *args,
         reward_tokens: Float['b d'] | None = None,
-        cond_scale = 1.,
+        cached_state_keys_values = (None, None),
+        cond_scale = 0.,
+        remove_parallel_component = False,
+        keep_parallel_frac = 0.,
+        return_state_keys_values = True,
+
         **kwargs
     ):
+        assert return_state_keys_values, 'cached key values must be turned on'
+
+        with_reward_cache, without_reward_cache = cached_state_keys_values
 
-        out = self.forward(
+        maybe_reward_out = self.forward(
             *args,
             reward_tokens = reward_tokens,
+            cached_state_keys_values = with_reward_cache,
+            return_state_keys_values = return_state_keys_values,
             **kwargs
         )
 
-        if not exists(reward_tokens) or cond_scale == 1.:
-            return out
+        action_flow_with_reward, with_reward_cache_kv = maybe_reward_out
 
-        raise NotImplementedError
+        if not exists(reward_tokens) or cond_scale == 0.:
+            return action_flow_with_reward, (with_reward_cache_kv, None)
+
+        no_reward_out = self.forward(
+            *args,
+            cached_state_keys_values = without_reward_cache,
+            return_state_keys_values = return_state_keys_values,
+            **kwargs
+        )
+
+        action_flow_without_reward, without_reward_cache_kv = no_reward_out
+
+        update = action_flow_with_reward - action_flow_without_reward
+
+        if remove_parallel_component:
+            # from https://arxiv.org/abs/2410.02416
+
+            update_parallel, update_orthog = project(update, action_flow_with_reward)
+            update = update_orthog + update_parallel * keep_parallel_frac
+
+        flow_with_reward_cfg = action_flow_with_reward + cond_scale * update
+
+        return flow_with_reward_cfg, (with_reward_cache_kv, without_reward_cache_kv)
 
     def forward(
         self,
diff --git a/pyproject.toml b/pyproject.toml
index e58be61..0ac4772 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [project]
 name = "pi-zero-pytorch"
-version = "0.0.17"
+version = "0.0.18"
 description = "π0 in Pytorch"
 authors = [
     { name = "Phil Wang", email = "lucidrains@gmail.com" }