```python
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline

_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor depth_min_bias_softmax_cuda(
    torch::Tensor x, torch::Tensor bias);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <math_constants.h>

__device__ __forceinline__ float minimum_propagate_nan(float a, float b) {
    return (isnan(b) || b < a) ? b : a;
}

template<int STATIC_DEPTH>
__global__ void depth_min_bias_softmax_vec4_kernel(
    const float4* __restrict__ input,
    const float4* __restrict__ bias,
    float4* __restrict__ output,
    int spatial,
    int dynamic_depth)
{
    constexpr int GROUP_SIZE = 8;
    constexpr int PIXELS_PER_BLOCK = 32;
    constexpr int CHANNEL_VECTORS = 6;

    const int channel_vector = threadIdx.x & (GROUP_SIZE - 1);
    const int position =
        blockIdx.x * PIXELS_PER_BLOCK + threadIdx.x / GROUP_SIZE;
    const int batch = blockIdx.y;
    const int depth = STATIC_DEPTH ? STATIC_DEPTH : dynamic_depth;
    const bool active = position < spatial && channel_vector < CHANNEL_VECTORS;

    float4 minimum = make_float4(
        CUDART_INF_F, CUDART_INF_F, CUDART_INF_F, CUDART_INF_F);

    if (active) {
        const int64_t base =
            (int64_t(batch) * depth * spatial + position) * CHANNEL_VECTORS
            + channel_vector;
        const int64_t depth_stride = int64_t(spatial) * CHANNEL_VECTORS;

        #pragma unroll
        for (int d = 0; d < (STATIC_DEPTH ? STATIC_DEPTH : dynamic_depth); ++d) {
            const float4 v = input[base + int64_t(d) * depth_stride];
            minimum.x = minimum_propagate_nan(minimum.x, v.x);
            minimum.y = minimum_propagate_nan(minimum.y, v.y);
            minimum.z = minimum_propagate_nan(minimum.z, v.z);
            minimum.w = minimum_propagate_nan(minimum.w, v.w);
        }

        const float4 b = bias[channel_vector];
        minimum.x += b.x;
        minimum.y += b.y;
        minimum.z += b.z;
        minimum.w += b.w;
    }

    float maximum = active
        ? fmaxf(fmaxf(minimum.x, minimum.y), fmaxf(minimum.z, minimum.w))
        : -CUDART_INF_F;

    #pragma unroll
    for (int offset = 4; offset > 0; offset >>= 1) {
        maximum = fmaxf(
            maximum,
            __shfl_xor_sync(0xffffffff, maximum, offset, GROUP_SIZE));
    }

    float4 exponential = make_float4(0.f, 0.f, 0.f, 0.f);
    if (active) {
        exponential.x = __expf(minimum.x - maximum);
        exponential.y = __expf(minimum.y - maximum);
        exponential.z = __expf(minimum.z - maximum);
        exponential.w = __expf(minimum.w - maximum);
    }

    float denominator =
        (exponential.x + exponential.y) + (exponential.z + exponential.w);

    #pragma unroll
    for (int offset = 4; offset > 0; offset >>= 1) {
        denominator +=
            __shfl_xor_sync(0xffffffff, denominator, offset, GROUP_SIZE);
    }

    if (active) {
        const float inverse = 1.f / denominator;
        exponential.x *= inverse;
        exponential.y *= inverse;
        exponential.z *= inverse;
        exponential.w *= inverse;

        const int64_t index =
            (int64_t(batch) * spatial + position) * CHANNEL_VECTORS
            + channel_vector;
        output[index] = exponential;
    }
}

torch::Tensor depth_min_bias_softmax_cuda(
    torch::Tensor x, torch::Tensor bias)
{
    TORCH_CHECK(x.is_cuda() && bias.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(
        x.scalar_type() == at::kFloat && bias.scalar_type() == at::kFloat,
        "Expected float32 tensors");
    TORCH_CHECK(
        x.dim() == 5 && x.size(1) == 24 && x.size(2) > 0,
        "Expected shape (N, 24, D, H, W)");
    TORCH_CHECK(
        x.is_contiguous(at::MemoryFormat::ChannelsLast3d),
        "Expected channels-last 3D storage");
    TORCH_CHECK(
        bias.numel() == 24 && bias.is_contiguous() &&
        bias.device() == x.device(),
        "Invalid bias");
    TORCH_CHECK(x.size(0) <= 65535, "Batch size exceeds launch limit");

    const c10::cuda::CUDAGuard guard(x.device());
    const int64_t spatial64 = x.size(3) * x.size(4);
    TORCH_CHECK(
        spatial64 <= 2147483616LL && x.size(2) <= 2147483647LL,
        "Tensor dimensions are too large");

    auto storage = torch::empty(
        {x.size(0), x.size(3), x.size(4), 24}, x.options());
    auto output = storage.permute({0, 3, 1, 2});

    if (storage.numel() == 0) {
        return output;
    }

    const int spatial = static_cast<int>(spatial64);
    const int depth = static_cast<int>(x.size(2));
    const dim3 grid(
        static_cast<unsigned int>((spatial64 + 31) / 32),
        static_cast<unsigned int>(x.size(0)));
    const auto stream = at::cuda::getCurrentCUDAStream();

    const auto* input_ptr =
        reinterpret_cast<const float4*>(x.data_ptr<float>());
    const auto* bias_ptr =
        reinterpret_cast<const float4*>(bias.data_ptr<float>());
    auto* output_ptr =
        reinterpret_cast<float4*>(storage.data_ptr<float>());

    if (depth == 22) {
        depth_min_bias_softmax_vec4_kernel<22><<<grid, 256, 0, stream>>>(
            input_ptr, bias_ptr, output_ptr, spatial, depth);
    } else {
        depth_min_bias_softmax_vec4_kernel<0><<<grid, 256, 0, stream>>>(
            input_ptr, bias_ptr, output_ptr, spatial, depth);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_fused_ops = load_inline(
    name="conv3d_channels_last_min_bias_softmax_vec4_v4",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depth_min_bias_softmax_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, dim):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.conv.to(memory_format=torch.channels_last_3d)
        self.dim = dim

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and self.conv.weight.dtype == torch.float32
            and self.conv.out_channels == 24
            and self.conv.bias is not None
            and self.dim in (2, -3)
            and x.ndim == 5
            and x.shape[0] <= 65535
        ):
            x = x.contiguous(memory_format=torch.channels_last_3d)
            y = F.conv3d(
                x,
                self.conv.weight,
                None,
                self.conv.stride,
                self.conv.padding,
                self.conv.dilation,
                self.conv.groups,
            )
            if y.dtype == torch.float32:
                y = y.contiguous(memory_format=torch.channels_last_3d)
                return _fused_ops.depth_min_bias_softmax_cuda(
                    y, self.conv.bias
                )

            y = y + self.conv.bias.to(y.dtype).view(1, -1, 1, 1, 1)
            return torch.softmax(torch.min(y, dim=self.dim)[0], dim=1)

        y = self.conv(x)
        return torch.softmax(torch.min(y, dim=self.dim)[0], dim=1)
```