diff --git a/tests/test_optimizers.py b/tests/test_optimizers.py
index e51ead764..3ab10533c 100644
--- a/tests/test_optimizers.py
+++ b/tests/test_optimizers.py
@@ -1,4 +1,5 @@
 import copy
+import warnings
 from collections.abc import Callable
 from functools import partial
 from typing import Any, get_args
@@ -1086,6 +1087,57 @@ def test_frechet_cell_fire_optimization(
     )
 
 
+def test_frechet_lbfgs_clamps_extreme_deformation(
+    ar_supercell_sim_state: SimState, lj_model: ModelInterface
+) -> None:
+    """LBFGS + Frechet cell filter clamps extreme log-space deformation.
+
+    Injects extreme cell_positions so that cell_positions / cell_factor > 2.0,
+    then verifies: (1) the clamp warning fires, (2) the log-space deformation
+    is bounded after the step, and (3) positions/cell remain finite.
+    """
+    state = ts.lbfgs_init(
+        state=ar_supercell_sim_state,
+        model=lj_model,
+        cell_filter=ts.CellFilter.frechet,
+    )
+
+    # Inject extreme cell_positions: log-deform = cell_positions/cell_factor = 10
+    # This far exceeds the MAX_LOG_DEFORM=2.0 clamp threshold.
+    state.cell_positions = state.cell_positions + 10.0 * state.cell_factor.view(
+        -1, 1, 1
+    ) * torch.eye(3, device=state.cell.device, dtype=state.cell.dtype).unsqueeze(0)
+
+    log_deform_before = (
+        (state.cell_positions / state.cell_factor.view(-1, 1, 1)).abs().max().item()
+    )
+    assert log_deform_before > 5.0, "Setup: log-deform should be extreme before step"
+
+    with warnings.catch_warnings(record=True) as caught_warnings:
+        warnings.simplefilter("always")
+        state = ts.lbfgs_step(state=state, model=lj_model)
+
+    # 1. Log-space deformation must be bounded after the clamp
+    log_deform_after = (
+        (state.cell_positions / state.cell_factor.view(-1, 1, 1)).abs().max().item()
+    )
+    assert log_deform_after <= 2.5, (
+        f"Log-space deformation should be clamped to ~2.0, got {log_deform_after:.2f}"
+    )
+
+    # 2. Positions and cell must remain finite
+    assert not torch.isnan(state.positions).any(), "Positions contain NaN"
+    assert not torch.isinf(state.positions).any(), "Positions contain Inf"
+    assert not torch.isnan(state.cell).any(), "Cell contains NaN"
+    assert not torch.isinf(state.cell).any(), "Cell contains Inf"
+
+    # 3. The clamp warning must have fired
+    clamp_warnings = [
+        warn for warn in caught_warnings if "Clamping log-space" in str(warn.message)
+    ]
+    assert len(clamp_warnings) > 0, "Expected clamping warning but none was emitted"
+
+
 @pytest.mark.parametrize(
     "filter_func",
     [None, ts.CellFilter.unit, ts.CellFilter.frechet],
diff --git a/torch_sim/optimizers/bfgs.py b/torch_sim/optimizers/bfgs.py
index 5cccf96ca..c3a344cf3 100644
--- a/torch_sim/optimizers/bfgs.py
+++ b/torch_sim/optimizers/bfgs.py
@@ -20,7 +20,11 @@
 
 import torch_sim as ts
 from torch_sim.optimizers import cell_filters
-from torch_sim.optimizers.cell_filters import CellBFGSState, frechet_cell_filter_init
+from torch_sim.optimizers.cell_filters import (
+    CellBFGSState,
+    _clamp_deform_grad_log,
+    frechet_cell_filter_init,
+)
 from torch_sim.state import SimState
 
 
@@ -507,6 +511,10 @@ def bfgs_step(  # noqa: C901, PLR0915
             # Frechet: deform_grad = exp(cell_positions / cell_factor)
             cell_factor_reshaped = state.cell_factor.view(state.n_systems, 1, 1)
             deform_grad_log_new = cell_positions_new / cell_factor_reshaped  # [S, 3, 3]
+            deform_grad_log_new, cell_positions_new = _clamp_deform_grad_log(
+                deform_grad_log_new, cell_positions_new, cell_factor_reshaped
+            )
+            state.cell_positions = cell_positions_new  # [S, 3, 3]
             deform_grad_new = torch.matrix_exp(deform_grad_log_new)  # [S, 3, 3]
         else:
             # UnitCell: deform_grad = cell_positions / cell_factor
diff --git a/torch_sim/optimizers/cell_filters.py b/torch_sim/optimizers/cell_filters.py
index b501a7aa8..8a58f8d40 100644
--- a/torch_sim/optimizers/cell_filters.py
+++ b/torch_sim/optimizers/cell_filters.py
@@ -6,6 +6,7 @@
 during optimization.
 """
 
+import warnings
 from collections.abc import Callable
 from dataclasses import dataclass, field
 from enum import StrEnum
@@ -19,6 +20,46 @@
 from torch_sim.state import SimState
 
 
+MAX_LOG_DEFORM = 2.0
+
+
+def _clamp_deform_grad_log(
+    deform_grad_log: torch.Tensor,
+    cell_positions: torch.Tensor,
+    cell_factor_reshaped: torch.Tensor,
+    *,
+    max_log_deform: float = MAX_LOG_DEFORM,
+) -> tuple[torch.Tensor, torch.Tensor]:
+    """Clamp log-space deformation gradient to prevent matrix_exp overflow.
+
+    When cell_positions grow unbounded (from diverging structures or extreme
+    steps), matrix_exp overflows to Inf/NaN. This clamps the log-space values
+    and writes back the clamped cell_positions so they don't re-accumulate.
+
+    Args:
+        deform_grad_log: Log of the deformation gradient, shape (S, 3, 3).
+        cell_positions: Current cell positions in log space, shape (S, 3, 3).
+        cell_factor_reshaped: Cell factor broadcast to (S, 1, 1).
+        max_log_deform: Maximum absolute value for log-space entries.
+
+    Returns:
+        Tuple of (clamped deform_grad_log, clamped cell_positions).
+    """
+    exceeds = deform_grad_log.abs() > max_log_deform
+    if exceeds.any():
+        n_clamped = int(exceeds.any(dim=(-2, -1)).sum().item())
+        warnings.warn(
+            f"Clamping log-space deformation gradient for {n_clamped} "
+            f"system(s) to [-{max_log_deform}, {max_log_deform}] "
+            f"(max |log(F)| = {deform_grad_log.abs().max().item():.2f}). "
+            f"This prevents matrix_exp overflow from diverging cell optimization.",
+            stacklevel=3,
+        )
+        deform_grad_log = deform_grad_log.clamp(-max_log_deform, max_log_deform)
+        cell_positions = deform_grad_log * cell_factor_reshaped
+    return deform_grad_log, cell_positions
+
+
 def _setup_cell_factor(
     state: SimState,
     cell_factor: float | torch.Tensor | None,
@@ -294,6 +335,9 @@ def frechet_cell_step[T: AnyCellState](state: T, cell_lr: float | torch.Tensor)
     # Convert from log space to deformation gradient
     cell_factor_reshaped = state.cell_factor.view(state.n_systems, 1, 1)
     deform_grad_log_new = cell_positions_new / cell_factor_reshaped
+    deform_grad_log_new, cell_positions_new = _clamp_deform_grad_log(
+        deform_grad_log_new, cell_positions_new, cell_factor_reshaped
+    )
     deform_grad_new = torch.matrix_exp(deform_grad_log_new)
 
     # Update cell from new deformation gradient
@@ -336,6 +380,10 @@ def compute_cell_forces[T: AnyCellState](
         deform_grad_log = tsm.matrix_log_33(
             cur_deform_grad, sim_dtype=cur_deform_grad.dtype
         )
+        # Clamp to the same limit used in lbfgs_step to prevent NaN from
+        # propagating into expm_frechet. Systems hitting the clamp have
+        # diverging cells; their cell forces will be approximate but finite.
+        deform_grad_log = deform_grad_log.clamp(-MAX_LOG_DEFORM, MAX_LOG_DEFORM)
         frechet_method = getattr(state, "frechet_method", None)
         cell_forces = _frechet_cell_forces(
             deform_grad_log, ucf_cell_grad, frechet_method=frechet_method
diff --git a/torch_sim/optimizers/fire.py b/torch_sim/optimizers/fire.py
index e35ec1c18..8efcb3a7b 100644
--- a/torch_sim/optimizers/fire.py
+++ b/torch_sim/optimizers/fire.py
@@ -8,6 +8,7 @@
 import torch_sim.math as tsm
 from torch_sim._duecredit import dcite
 from torch_sim.optimizers import CellFireState, cell_filters
+from torch_sim.optimizers.cell_filters import _clamp_deform_grad_log
 from torch_sim.state import SimState
 
 
@@ -428,6 +429,10 @@ def _ase_fire_step[T: "FireState | CellFireState"](  # noqa: C901, PLR0915
             if is_frechet:  # Frechet: convert from log space to deformation gradient
                 cell_factor_reshaped = state.cell_factor.view(state.n_systems, 1, 1)
                 deform_grad_log_new = cell_positions_new / cell_factor_reshaped
+                deform_grad_log_new, cell_positions_new = _clamp_deform_grad_log(
+                    deform_grad_log_new, cell_positions_new, cell_factor_reshaped
+                )
+                state.cell_positions = cell_positions_new
                 deform_grad_new = torch.matrix_exp(deform_grad_log_new)
             else:  # Unit cell: positions are scaled deformation gradient
                 cell_factor_expanded = state.cell_factor.expand(state.n_systems, 3, 1)
diff --git a/torch_sim/optimizers/lbfgs.py b/torch_sim/optimizers/lbfgs.py
index 0221f92d7..f8413399c 100644
--- a/torch_sim/optimizers/lbfgs.py
+++ b/torch_sim/optimizers/lbfgs.py
@@ -18,6 +18,7 @@
 import torch_sim as ts
 from torch_sim.optimizers.cell_filters import (
     CellLBFGSState,
+    _clamp_deform_grad_log,
     compute_cell_forces,
     deform_grad,
     frechet_cell_filter_init,
@@ -486,7 +487,6 @@ def lbfgs_step(  # noqa: PLR0915, C901
         # Apply cell step
         dr_cell = step_cell  # [S, 3, 3]
         cell_positions_new = state.cell_positions + dr_cell  # [S, 3, 3]
-        state.cell_positions = cell_positions_new  # [S, 3, 3]
 
         # Determine if Frechet filter
         init_fn, _step_fn = state.cell_filter
@@ -496,12 +496,17 @@ def lbfgs_step(  # noqa: PLR0915, C901
             # Frechet: deform_grad = exp(cell_positions / cell_factor)
             cell_factor_reshaped = state.cell_factor.view(n_systems, 1, 1)
             deform_grad_log_new = cell_positions_new / cell_factor_reshaped  # [S, 3, 3]
+            deform_grad_log_new, cell_positions_new = _clamp_deform_grad_log(
+                deform_grad_log_new, cell_positions_new, cell_factor_reshaped
+            )
             deform_grad_new = torch.matrix_exp(deform_grad_log_new)  # [S, 3, 3]
         else:
             # UnitCell: deform_grad = cell_positions / cell_factor
             cell_factor_expanded = state.cell_factor.expand(n_systems, 3, 1)
             deform_grad_new = cell_positions_new / cell_factor_expanded  # [S, 3, 3]
 
+        state.cell_positions = cell_positions_new  # [S, 3, 3]
+
         # Update cell: new_cell = reference_cell @ deform_grad^T
         # Use set_constrained_cell to apply cell constraints (e.g. FixSymmetry)
         new_col_vector_cell = torch.bmm(