diff --git a/flux_train.py b/flux_train.py
index 4aa67220..14fb5cc8 100644
--- a/flux_train.py
+++ b/flux_train.py
@@ -330,6 +330,8 @@ def train(args):
     # 学習に必要なクラスを準備する
     accelerator.print("prepare optimizer, data loader etc.")
 
+    fused_optimizers_supported = ['adafactor', 'adamoffload', 'nadamoffload', 'adamwoffload', 'nadamwoffload']
+
     if args.blockwise_fused_optimizers:
         # fused backward pass: https://pytorch.org/tutorials/intermediate/optimizer_step_in_backward_tutorial.html
         # Instead of creating an optimizer for all parameters as in the tutorial, we create an optimizer for each block of parameters.
@@ -381,10 +383,25 @@ def train(args):
             raise ValueError("Schedule-free optimizer is not supported with blockwise fused optimizers")
         optimizer_train_fn = lambda: None  # dummy function
         optimizer_eval_fn = lambda: None  # dummy function
+
+        if (args.optimizer_type in fused_optimizers_supported) and args.full_bf16:
+            logger.warning("Use of --blockwise_fused_optimizers is preventing stochastic/Kahan weight updates.")
     else:
         _, _, optimizer = train_util.get_optimizer(args, trainable_params=params_to_optimize)
         optimizer_train_fn, optimizer_eval_fn = train_util.get_optimizer_train_eval_fn(optimizer, args)
 
+    # Pass any Kahan summation arg to the optimizer
+    if args.kahan_summation:
+        # Self check parameter compatibility
+        if args.optimizer_type.lower() not in fused_optimizers_supported:
+            logger.warning("Kahan summation has been requested, but this is not supported by the selected optimizer.")
+        if not args.full_bf16:
+            logger.warning("Kahan summation requires --full_bf16")
+        if args.blockwise_fused_optimizers:
+            logger.warning("Kahan summation has been requested, but these are not compatible with --blockwise_fused_optimizer. "\
+                           "Perhaps try --fused_backward_pass instead.")
+    optimizer.use_kahan_summation = args.kahan_summation
+
     # prepare dataloader
     # strategies are set here because they cannot be referenced in another process. Copy them with the dataset
     # some strategies can be None
@@ -437,6 +454,13 @@ def train(args):
         ), "full_bf16 requires mixed precision='bf16' / full_bf16を使う場合はmixed_precision='bf16'を指定してください。"
         accelerator.print("enable full bf16 training.")
         flux.to(weight_dtype)
+
+        # Experimental: some layers have very few weights, and training quality seems
+        # to increase significantly if these are left in f32 format while training.
+        if args.fused_backward_pass:
+            flux.final_layer.linear.to(dtype=torch.float32)  # Loses lower bits from some saved files,
+            flux.img_in            .to(dtype=torch.float32)  # but most saved models aren't f32/f16 anyway.
+
         if clip_l is not None:
             clip_l.to(weight_dtype)
             t5xxl.to(weight_dtype)
@@ -474,10 +498,18 @@ def train(args):
     train_util.resume_from_local_or_hf_if_specified(accelerator, args)
 
     if args.fused_backward_pass:
-        # use fused optimizer for backward pass: other optimizers will be supported in the future
+        # use fused optimizer for backward pass. Only some specific optimizers are supported.
         import library.adafactor_fused
+        import library.adamw_fused
 
-        library.adafactor_fused.patch_adafactor_fused(optimizer)
+        if args.optimizer_type.lower() == "adafactor":
+            library.adafactor_fused.patch_adafactor_fused(optimizer)
+        elif args.optimizer_type.lower() == "adamoffload" or args.optimizer_type.lower() == "adamwoffload":
+            library.adamw_fused.patch_adamw_offload_fused(optimizer, False)
+        elif args.optimizer_type.lower() == "nadamoffload" or args.optimizer_type.lower() == "nadamwoffload":
+            library.adamw_fused.patch_adamw_offload_fused(optimizer, True)  # Nesterov
+        else:
+            logger.error(f"Optimizer '{args.optimizer_type}' does not have a --fused_backward_pass implementation available")
 
         for param_group, param_name_group in zip(optimizer.param_groups, param_names):
             for parameter, param_name in zip(param_group["params"], param_name_group):
@@ -816,6 +848,12 @@ def setup_parser() -> argparse.ArgumentParser:
         action="store_true",
         help="enable blockwise optimizers for fused backward pass and optimizer step / fused backward passとoptimizer step のためブロック単位のoptimizerを有効にする",
     )
+    parser.add_argument(
+        "--kahan_summation",
+        action="store_true",
+        help="Offloads to CPU the float part lost during bf16 quantization, and re-adds it to the next step / "\
+            "bf16 量子化中に失われた浮動小数点部分を CPU にオフロードし、次のステップに再度追加します",
+    )
     parser.add_argument(
         "--skip_latents_validity_check",
         action="store_true",
diff --git a/library/adafactor_fused.py b/library/adafactor_fused.py
index b5afa236..6dfd0174 100644
--- a/library/adafactor_fused.py
+++ b/library/adafactor_fused.py
@@ -28,6 +28,62 @@ def copy_stochastic_(target: torch.Tensor, source: torch.Tensor):
     del result
 
 
+# Kahan summation for bfloat16
+# The implementation was provided by araleza.
+# Based on paper "Revisiting BFloat16 Training": https://arxiv.org/pdf/2010.06192
+
+def copy_kahan_(target: torch.Tensor, source: torch.Tensor, state, update):
+    """
+    Copies source into target using Kahan summation.
+
+    The lower bits of the float32 weight that are lost on conversion to bfloat16
+    are sent to the CPU until the next step, where they are re-added onto the weights
+    before adding the gradient update.  This produces near float32-like weight behavior,
+    although the copies back and forth to main memory result in slower training steps.
+
+    Args:
+        target: the target tensor with dtype=bfloat16
+        source: the target tensor with dtype=float32
+        state:  the optimizer state, used to store kahan residuals
+        update: the change in weights due to the gradient
+    """
+
+    # Initialize residuals to 0 for first step
+    if state.get('kahan_residuals') is None:
+        state['kahan_residuals'] = torch.zeros_like(source, dtype=torch.int16)
+    
+    # Need this in 32 bit as PyTorch doesn't support mixed 32-bit and 16-bit math operations
+    state['kahan_residuals'] = state['kahan_residuals'].to(source.device).to(dtype=torch.int32)
+    
+    # Bring the previous step's lower bits of the weights back from the
+    # cpu device, and add them back to the weights of the current step.
+    source_i32 = source.view(dtype=torch.int32)  # Can't do math on uint32
+    source_i32.add_(state['kahan_residuals'])
+
+    # Reverse any rounding up during the cast to bf16 on the previous step
+    rounded_up = state['kahan_residuals'] >= 32768
+    source_i32[rounded_up] -= 65536
+
+    # Must add the gradient update after the bottom bits are restored in case
+    # the exponent is changed by the update, or the -65536 on the line above
+    # would drop the uint32 value below zero, which is invalid.
+    source.add_(-update)
+
+    # Get the lower bits into the residual
+    torch.bitwise_and(source_i32, 0x0000FFFF, out=state['kahan_residuals'])
+
+    # Ensure rounding to bfloat16 matches expectations. These lines may not be
+    # necessary as target.copy_ should do this rounding anyway.
+    source_i32.add_(32768)  # Add offset so clipping bits performs round-to-nearest
+    source_i32.bitwise_and_(-65536)  # -65536 = FFFF0000 as a signed int32. Leaves only upper bits in source
+
+    # Move the 16-bit Kahan bits from VRAM to main memory
+    state['kahan_residuals'] = state['kahan_residuals'].to(dtype=torch.uint16).to("cpu")
+
+    # Copy the quantized floats into the target tensor
+    target.copy_(source)
+
+
 @torch.no_grad()
 def adafactor_step_param(self, p, group):
     if p.grad is None:
@@ -102,13 +158,19 @@ def adafactor_step_param(self, p, group):
     if group["weight_decay"] != 0:
         p_data_fp32.add_(p_data_fp32, alpha=(-group["weight_decay"] * lr))
 
-    p_data_fp32.add_(-update)
+    # Add on gradient update, but not if using kahan summation as the bottom
+    # bits must be restored first. (This update occurs in copy_kahan_() instead)
+    if not self.optimizer.use_kahan_summation:
+        p_data_fp32.add_(-update)
 
     # if p.dtype in {torch.float16, torch.bfloat16}:
     #    p.copy_(p_data_fp32)
 
     if p.dtype == torch.bfloat16:
-        copy_stochastic_(p, p_data_fp32)
+        if self.optimizer.use_kahan_summation:
+            copy_kahan_(p, p_data_fp32, state, update)
+        else:
+            copy_stochastic_(p, p_data_fp32)
     elif p.dtype == torch.float16:
         p.copy_(p_data_fp32)
 
diff --git a/library/adamw_fused.py b/library/adamw_fused.py
new file mode 100644
index 00000000..8419d422
--- /dev/null
+++ b/library/adamw_fused.py
@@ -0,0 +1,192 @@
+import math
+import torch
+
+from library.adafactor_fused import copy_stochastic_
+from library.adafactor_fused import copy_kahan_
+
+
+def to_float24_bytes(tensor_f32: torch.Tensor) -> torch.Tensor:
+    """
+    Converts a float32 tensor to a 'float24' representation for storage.
+
+    This is done by taking the 3 most significant bytes of each float32 element.
+    On a little-endian system, these are the last 3 bytes.
+    # TODO - Check this works on Mac, which is a big-endian system
+
+    Args:
+        tensor_f32: The input tensor with dtype torch.float32.
+
+    Returns:
+        A 1D tensor of dtype torch.uint8 containing the packed 'float24' data.
+    """
+    if tensor_f32.dtype != torch.float32:
+        raise TypeError("Input tensor must be of dtype torch.float32")
+
+    tensor_u8 = tensor_f32.view(torch.uint8)
+    tensor_u8_reshaped = tensor_u8.view(-1, 4)
+    tensor_f24_bytes = tensor_u8_reshaped[:, 1:]
+    return tensor_f24_bytes.flatten()
+
+
+def from_float24_bytes(tensor_f24_u8: torch.Tensor, original_shape: torch.Size) -> torch.Tensor:
+    """
+    Restores a 'float24' byte tensor back to a float32 tensor.
+
+    Args:
+        tensor_f24_u8: A 1D tensor of dtype torch.uint8 from to_float24_bytes.
+        original_shape: The shape of the original float32 tensor.
+        device: The device to create the restored tensor on.
+
+    Returns:
+        The restored tensor with dtype torch.float32 and the original shape.
+    """
+    if tensor_f24_u8.dtype != torch.uint8:
+        raise TypeError("Input byte tensor must be of dtype torch.uint8")
+    if tensor_f24_u8.numel() % 3 != 0:
+        raise ValueError("Input byte tensor size must be a multiple of 3")
+    
+    tensor_u8_3bytes = tensor_f24_u8.view(-1, 3)
+    padding = torch.zeros(tensor_u8_3bytes.shape[0], 1, dtype=torch.uint8, device=tensor_u8_3bytes.device)
+    tensor_u8_4bytes = torch.cat([padding, tensor_u8_3bytes], dim=1)
+    tensor_f32_flat = tensor_u8_4bytes.flatten().view(torch.float32)
+    return tensor_f32_flat.view(original_shape)
+
+
+@torch.no_grad()
+def adamw_offload_step_param(self, p, group):
+
+    if p.grad is None:
+        return
+    grad = p.grad
+    if grad.dtype in {torch.float16, torch.bfloat16}:
+        grad = grad.float()
+    if grad.is_sparse:
+        raise RuntimeError("This (N)AdamW implementation does not support sparse gradients.")
+
+    state = self.state[p]
+    grad_shape = grad.shape
+
+    p_data_fp32 = p
+    if p.dtype in {torch.float16, torch.bfloat16}:
+        p_data_fp32 = p_data_fp32.float()
+    
+    # Tensors with few elements may be more sensitive to quantization
+    # errors, so keep them in float32
+    high_quality = torch.numel(p) <= 4096
+
+    # State Initialization
+    if len(state) == 0:
+        state["step"] = 0
+
+        data_type = torch.float32 if high_quality else torch.uint16
+
+        state['exp_avg']    = torch.zeros_like(p, dtype=data_type)
+        state['exp_avg_sq'] = torch.zeros_like(p, dtype=data_type)
+
+    state["step"] += 1
+
+    # NAdam
+
+    beta1, beta2 = group['betas']
+    eps = group['eps']  # 1e-8
+    weight_decay = group.get('weight_decay', 0.0)
+
+    # Bias correction terms
+    bias_correction1 = 1.0 - math.pow(beta1, state['step'])
+    bias_correction2 = 1.0 - math.pow(beta2, state['step'])
+        
+    eps_p2: float = math.pow(eps, 2)
+
+    # Bring state back (from CPU, if necessary)
+
+    # Recover the exp avg states from however they're stored
+    def unpack_tensor(state, key, target_device):
+
+        # Stored as f24 format?
+        if state[f'{key}'].dtype == torch.uint8:
+            return from_float24_bytes(state[f'{key}'].to(target_device), state[f'{key}_shape'])
+
+        # bf16 / u16 / f32
+        return state[f'{key}'].to(target_device).to(dtype=torch.float32)
+
+    state['exp_avg']    = unpack_tensor(state, 'exp_avg',    p.device)
+    state['exp_avg_sq'] = unpack_tensor(state, 'exp_avg_sq', p.device)
+    exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
+
+    # Update biased first and second moment estimates
+    exp_avg   .mul_(beta1).add_    (grad,       alpha=1.0 - beta1)
+    exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1.0 - beta2)
+
+    # Compute bias-corrected second moment for denominator
+    exp_avg_sq_corrected = exp_avg_sq / bias_correction2
+
+    # Compute update based on whether Nesterov momentum (NAdam) is being used
+    if self.use_nesterov:
+        # The next step's bias correction for momentum is needed
+        bias_correction1_next = 1.0 - math.pow(beta1, state['step'] + 1)
+
+        # NAdam update: combines current gradient with momentum look-ahead
+        momentum_cache = exp_avg / bias_correction1_next
+        update = (beta1 * momentum_cache + (1.0 - beta1) * grad / bias_correction1) / (exp_avg_sq_corrected.sqrt() + eps)
+    else:
+        # Standard Adam update: use bias-corrected first moment directly
+        exp_avg_corrected = exp_avg / bias_correction1
+        update = exp_avg_corrected / (exp_avg_sq_corrected.sqrt() + eps)
+
+    lr: float = group['lr']
+    
+    # Apply learning rate
+    update.mul_(lr)
+
+    # Apply weight decay
+    if weight_decay != 0:
+        p_data_fp32.mul_(1 - lr * weight_decay)
+
+    # Reduce the size of large exp_avg and exp_avg_sq tensors to 24-bit,
+    # and then move them to cpu memory
+    if not high_quality:
+        state[f'exp_avg_shape'] = state[f'exp_avg'].shape
+        state[f'exp_avg'] = to_float24_bytes(state[f'exp_avg']).to('cpu')
+
+        state[f'exp_avg_sq_shape'] = state[f'exp_avg_sq'].shape
+        state[f'exp_avg_sq'] = to_float24_bytes(state[f'exp_avg_sq']).to('cpu')
+
+    # Add on gradient update, but not if using kahan summation as the bottom
+    # bits must be restored first. (This update occurs in copy_kahan_() instead)
+    if not self.optimizer.use_kahan_summation:
+        p_data_fp32.add_(-update)
+
+    if p.dtype == torch.bfloat16:
+        if self.optimizer.use_kahan_summation:
+            copy_kahan_(p, p_data_fp32, state, update)
+        else:
+            copy_stochastic_(p, p_data_fp32)
+    elif p.dtype == torch.float16:
+        p.copy_(p_data_fp32)
+
+
+@torch.no_grad()
+def adamw_offload_step(self, closure=None):
+    """
+    Performs a single optimization step
+
+    Arguments:
+        closure (callable, optional): A closure that reevaluates the model
+            and returns the loss.
+    """
+    loss = None
+    if closure is not None:
+        loss = closure()
+
+    for group in self.param_groups:
+        for p in group["params"]:
+            adamw_offload_step_param(self, p, group)
+
+    return loss
+
+
+def patch_adamw_offload_fused(optimizer, use_nesterov):
+    optimizer.use_nesterov = use_nesterov
+
+    optimizer.step_param = adamw_offload_step_param.__get__(optimizer)
+    optimizer.step = adamw_offload_step.__get__(optimizer)
diff --git a/library/train_util.py b/library/train_util.py
index 756d88b1..7c00f7d1 100644
--- a/library/train_util.py
+++ b/library/train_util.py
@@ -4884,9 +4884,6 @@ def get_optimizer(args, trainable_params) -> tuple[str, str, object]:
     optimizer_type = optimizer_type.lower()
 
     if args.fused_backward_pass:
-        assert (
-            optimizer_type == "Adafactor".lower()
-        ), "fused_backward_pass currently only works with optimizer_type Adafactor / fused_backward_passは現在optimizer_type Adafactorでのみ機能します"
         assert (
             args.gradient_accumulation_steps == 1
         ), "fused_backward_pass does not work with gradient_accumulation_steps > 1 / fused_backward_passはgradient_accumulation_steps>1では機能しません"
@@ -5130,6 +5127,18 @@ def get_optimizer(args, trainable_params) -> tuple[str, str, object]:
         optimizer_class = transformers.optimization.Adafactor
         optimizer = optimizer_class(trainable_params, lr=lr, **optimizer_kwargs)
 
+    elif optimizer_type.lower() == "adamoffload" or optimizer_type.lower() == "nadamoffload":
+        logger.info(f"use [N]AdamOffload optimizer | {optimizer_kwargs}")
+
+        optimizer_class = torch.optim.Adam
+        optimizer = optimizer_class(trainable_params, lr=lr, **optimizer_kwargs)
+
+    elif optimizer_type.lower() == "adamwoffload" or optimizer_type.lower() == "nadamwoffload":
+        logger.info(f"use [N]AdamWOffload optimizer | {optimizer_kwargs}")
+
+        optimizer_class = torch.optim.AdamW  # default weight_decay seems to be 0.01
+        optimizer = optimizer_class(trainable_params, lr=lr, **optimizer_kwargs)
+
     elif optimizer_type == "AdamW".lower():
         logger.info(f"use AdamW optimizer | {optimizer_kwargs}")
         optimizer_class = torch.optim.AdamW