diff --git a/src/gfn/containers/__init__.py b/src/gfn/containers/__init__.py
index f3c3c9a5..0acaab06 100644
--- a/src/gfn/containers/__init__.py
+++ b/src/gfn/containers/__init__.py
@@ -1,3 +1,3 @@
-from .replay_buffer import ReplayBuffer
+from .replay_buffer import ReplayBuffer, PrioritizedReplayBuffer
 from .trajectories import Trajectories
 from .transitions import Transitions
diff --git a/src/gfn/containers/replay_buffer.py b/src/gfn/containers/replay_buffer.py
index c1679d9a..2cf9fcc6 100644
--- a/src/gfn/containers/replay_buffer.py
+++ b/src/gfn/containers/replay_buffer.py
@@ -18,7 +18,6 @@ class ReplayBuffer:
 
     Attributes:
         env: the Environment instance.
-        loss_fn: the Loss instance
         capacity: the size of the buffer.
         training_objects: the buffer of objects used for training.
         terminating_states: a States class representation of $s_f$.
@@ -56,13 +55,12 @@ def __init__(
             raise ValueError(f"Unknown objects_type: {objects_type}")
 
         self._is_full = False
-        self._index = 0
 
     def __repr__(self):
         return f"ReplayBuffer(capacity={self.capacity}, containing {len(self)} {self.objects_type})"
 
     def __len__(self):
-        return self.capacity if self._is_full else self._index
+        return len(self.training_objects)
 
     def add(self, training_objects: Transitions | Trajectories | tuple[States]):
         """Adds a training object to the buffer."""
@@ -73,8 +71,7 @@ def add(self, training_objects: Transitions | Trajectories | tuple[States]):
 
         to_add = len(training_objects)
 
-        self._is_full |= self._index + to_add >= self.capacity
-        self._index = (self._index + to_add) % self.capacity
+        self._is_full |= len(self) + to_add >= self.capacity
 
         self.training_objects.extend(training_objects)
         self.training_objects = self.training_objects[-self.capacity :]
@@ -102,6 +99,140 @@ def save(self, directory: str):
     def load(self, directory: str):
         """Loads the buffer from disk."""
         self.training_objects.load(os.path.join(directory, "training_objects"))
-        self._index = len(self.training_objects)
         if self.terminating_states is not None:
             self.terminating_states.load(os.path.join(directory, "terminating_states"))
+
+
+class PrioritizedReplayBuffer(ReplayBuffer):
+    """A replay buffer of trajectories or transitions.
+
+    Attributes:
+        env: the Environment instance.
+        capacity: the size of the buffer.
+        training_objects: the buffer of objects used for training.
+        terminating_states: a States class representation of $s_f$.
+        objects_type: the type of buffer (transitions, trajectories, or states).
+        cutoff_distance: threshold used to determine if new last_states are different
+            enough from those already contained in the buffer.
+        p_norm_distance: p-norm distance value to pass to torch.cdist, for the
+            determination of novel states.
+    """
+    def __init__(
+        self,
+        env: Env,
+        objects_type: Literal["transitions", "trajectories", "states"],
+        capacity: int = 1000,
+        cutoff_distance: float = 0.,
+        p_norm_distance: float = 1.,
+    ):
+        """Instantiates a prioritized replay buffer.
+        Args:
+            env: the Environment instance.
+            loss_fn: the Loss instance.
+            capacity: the size of the buffer.
+            objects_type: the type of buffer (transitions, trajectories, or states).
+            cutoff_distance: threshold used to determine if new last_states are
+                different enough from those already contained in the buffer. If the
+                cutoff is negative, all diversity caclulations are skipped (since all
+                norms are >= 0).
+            p_norm_distance: p-norm distance value to pass to torch.cdist, for the
+                determination of novel states.
+    """
+        super().__init__(env, objects_type, capacity)
+        self.cutoff_distance = cutoff_distance
+        self.p_norm_distance = p_norm_distance
+
+    def _add_objs(self, training_objects: Transitions | Trajectories | tuple[States]):
+        """Adds a training object to the buffer."""
+        # Adds the objects to the buffer.
+        self.training_objects.extend(training_objects)
+
+        # Sort elements by logreward, capping the size at the defined capacity.
+        ix = torch.argsort(self.training_objects.log_rewards)
+        self.training_objects = self.training_objects[ix]
+        self.training_objects = self.training_objects[-self.capacity :]
+
+        # Add the terminating states to the buffer.
+        if self.terminating_states is not None:
+            assert terminating_states is not None
+            self.terminating_states.extend(terminating_states)
+
+            # Sort terminating states by logreward as well.
+            self.terminating_states = self.terminating_states[ix]
+            self.terminating_states = self.terminating_states[-self.capacity :]
+
+    def add(self, training_objects: Transitions | Trajectories | tuple[States]):
+        """Adds a training object to the buffer."""
+        terminating_states = None
+        if isinstance(training_objects, tuple):
+            assert self.objects_type == "states" and self.terminating_states is not None
+            training_objects, terminating_states = training_objects
+
+        to_add = len(training_objects)
+        self._is_full |= len(self) + to_add >= self.capacity
+
+        # The buffer isn't full yet.
+        if len(self.training_objects) < self.capacity:
+            self._add_objs(training_objects)
+
+        # Our buffer is full and we will prioritize diverse, high reward additions.
+        else:
+            # Sort the incoming elements by their logrewards.
+            ix = torch.argsort(training_objects.log_rewards, descending=True)
+            training_objects = training_objects[ix]
+
+            # Filter all batch logrewards lower than the smallest logreward in buffer.
+            min_reward_in_buffer = self.training_objects.log_rewards.min()
+            idx_bigger_rewards = training_objects.log_rewards >= min_reward_in_buffer
+            training_objects = training_objects[idx_bigger_rewards]
+
+            # TODO: Concatenate input with final state for conditional GFN.
+            # if self.is_conditional:
+            #     batch = torch.cat(
+            #         [dict_curr_batch["input"], dict_curr_batch["final_state"]],
+            #         dim=-1,
+            #     )
+            #     buffer = torch.cat(
+            #         [self.storage["input"], self.storage["final_state"]],
+            #         dim=-1,
+            #     )
+
+            if self.cutoff_distance >= 0:
+                # Filter the batch for diverse final_states with high reward.
+                batch = training_objects.last_states.tensor.float()
+                batch_dim = training_objects.last_states.batch_shape[0]
+                batch_batch_dist = torch.cdist(
+                    batch.view(batch_dim, -1).unsqueeze(0),
+                    batch.view(batch_dim, -1).unsqueeze(0),
+                    p=self.p_norm_distance,
+                ).squeeze(0)
+
+                # Finds the min distance at each row, and removes rows below the cutoff.
+                r, w = torch.triu_indices(*batch_batch_dist.shape)  # Remove upper diag.
+                batch_batch_dist[r, w] = torch.finfo(batch_batch_dist.dtype).max
+                batch_batch_dist = batch_batch_dist.min(-1)[0]
+                idx_batch_batch = batch_batch_dist > self.cutoff_distance
+                training_objects = training_objects[idx_batch_batch]
+
+                # Compute all pairwise distances between the remaining batch & buffer.
+                batch = training_objects.last_states.tensor.float()
+                buffer = self.training_objects.last_states.tensor.float()
+                batch_dim = training_objects.last_states.batch_shape[0]
+                buffer_dim = self.training_objects.last_states.batch_shape[0]
+                batch_buffer_dist = (
+                    torch.cdist(
+                        batch.view(batch_dim, -1).unsqueeze(0),
+                        buffer.view(buffer_dim, -1).unsqueeze(0),
+                        p=self.p_norm_distance,
+                    )
+                    .squeeze(0)
+                    .min(-1)[0]  # Min calculated over rows - the batch elements.
+                )
+
+                # Filter the batch for diverse final_states w.r.t the buffer.
+                idx_batch_buffer = batch_buffer_dist > self.cutoff_distance
+                training_objects = training_objects[idx_batch_buffer]
+
+            # If any training object remain after filtering, add them.
+            if len(training_objects):
+                self._add_objs(training_objects)
diff --git a/src/gfn/containers/trajectories.py b/src/gfn/containers/trajectories.py
index 35196ec3..cc02bda1 100644
--- a/src/gfn/containers/trajectories.py
+++ b/src/gfn/containers/trajectories.py
@@ -90,7 +90,11 @@ def __init__(
             if when_is_done is not None
             else torch.full(size=(0,), fill_value=-1, dtype=torch.long)
         )
-        self._log_rewards = log_rewards
+        self._log_rewards = (
+            log_rewards
+            if log_rewards is not None
+            else torch.full(size=(0,), fill_value=0, dtype=torch.float)
+        )
         self.log_probs = (
             log_probs
             if log_probs is not None
@@ -232,22 +236,31 @@ def extend(self, other: Trajectories) -> None:
         self.states.extend(other.states)
         self.when_is_done = torch.cat((self.when_is_done, other.when_is_done), dim=0)
 
-        # For log_probs, we first need to make the first dimensions of self.log_probs and other.log_probs equal
-        # (i.e. the number of steps in the trajectories), and then concatenate them
+        # For log_probs, we first need to make the first dimensions of self.log_probs
+        # and other.log_probs equal (i.e. the number of steps in the trajectories), and
+        # then concatenate them.
         new_max_length = max(self.log_probs.shape[0], other.log_probs.shape[0])
         self.log_probs = self.extend_log_probs(self.log_probs, new_max_length)
         other.log_probs = self.extend_log_probs(other.log_probs, new_max_length)
-
         self.log_probs = torch.cat((self.log_probs, other.log_probs), dim=1)
 
+        # Concatenate log_rewards of the trajectories.
         if self._log_rewards is not None and other._log_rewards is not None:
             self._log_rewards = torch.cat(
                 (self._log_rewards, other._log_rewards),
                 dim=0,
             )
+        # Will not be None if object is initialized as empty.
         else:
             self._log_rewards = None
 
+        # Ensure log_probs/rewards are the correct dimensions. TODO: Remove?
+        if self.log_probs.numel() > 0:
+            assert self.log_probs.shape == self.actions.batch_shape
+
+        if self.log_rewards is not None:
+            assert len(self.log_rewards) == self.actions.batch_shape[-1]
+
         # Either set, or append, estimator outputs if they exist in the submitted
         # trajectory.
         if self.estimator_outputs is None and isinstance(
diff --git a/src/gfn/containers/transitions.py b/src/gfn/containers/transitions.py
index a3c920af..cbc214f6 100644
--- a/src/gfn/containers/transitions.py
+++ b/src/gfn/containers/transitions.py
@@ -90,7 +90,7 @@ def __init__(
             len(self.next_states.batch_shape) == 1
             and self.states.batch_shape == self.next_states.batch_shape
         )
-        self._log_rewards = log_rewards
+        self._log_rewards = log_rewards if log_rewards is not None else torch.zeros(0)
         self.log_probs = log_probs if log_probs is not None else torch.zeros(0)
 
     @property
@@ -208,10 +208,13 @@ def extend(self, other: Transitions) -> None:
         self.actions.extend(other.actions)
         self.is_done = torch.cat((self.is_done, other.is_done), dim=0)
         self.next_states.extend(other.next_states)
+
+        # Concatenate log_rewards of the trajectories.
         if self._log_rewards is not None and other._log_rewards is not None:
             self._log_rewards = torch.cat(
                 (self._log_rewards, other._log_rewards), dim=0
             )
+        # Will not be None if object is initialized as empty.
         else:
             self._log_rewards = None
         self.log_probs = torch.cat((self.log_probs, other.log_probs), dim=0)
diff --git a/tutorials/examples/train_hypergrid.py b/tutorials/examples/train_hypergrid.py
index 2041c7ca..eec3366b 100644
--- a/tutorials/examples/train_hypergrid.py
+++ b/tutorials/examples/train_hypergrid.py
@@ -17,7 +17,7 @@
 import wandb
 from tqdm import tqdm, trange
 
-from gfn.containers import ReplayBuffer
+from gfn.containers import ReplayBuffer, PrioritizedReplayBuffer
 from gfn.gflownet import (
     DBGFlowNet,
     FMGFlowNet,
@@ -185,12 +185,21 @@ def main(args):  # noqa: C901
             objects_type = "states"
         else:
             raise NotImplementedError(f"Unknown loss: {args.loss}")
-        replay_buffer = ReplayBuffer(
-            env, objects_type=objects_type, capacity=args.replay_buffer_size
-        )
 
-    # 3. Create the optimizer
+        if args.replay_buffer_prioritized:
+            replay_buffer = PrioritizedReplayBuffer(
+                env,
+                objects_type=objects_type,
+                capacity=args.replay_buffer_size,
+                p_norm_distance=1,  # Use L1-norm for diversity estimation.
+                cutoff_distance=0,  # -1 turns off diversity-based filtering.
+            )
+        else:
+            replay_buffer = ReplayBuffer(
+                env, objects_type=objects_type, capacity=args.replay_buffer_size
+            )
 
+    # 3. Create the optimizer
     # Policy parameters have their own LR.
     params = [
         {
@@ -292,6 +301,11 @@ def main(args):  # noqa: C901
         default=0,
         help="If zero, no replay buffer is used. Otherwise, the replay buffer is used.",
     )
+    parser.add_argument(
+        "--replay_buffer_prioritized",
+        action="store_true",
+        help="If set and replay_buffer_size > 0, use a prioritized replay buffer.",
+    )
 
     parser.add_argument(
         "--loss",